LMFDB - Embedded newform 37.9.d.a.6.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,9,Mod(6,37)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("37.6");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	37.d (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.0730085723$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$25$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			6.16
Character	$\chi$	$=$	37.6
Dual form			37.9.d.a.31.16

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.39144 - 6.39144i) q^{2} +92.4393i q^{3} +174.299i q^{4} +(596.761 + 596.761i) q^{5} +(590.820 + 590.820i) q^{6} -3526.08 q^{7} +(2750.23 + 2750.23i) q^{8} -1984.02 q^{9} +O(q^{10})$	\(q+(6.39144 - 6.39144i) q^{2} +92.4393i q^{3} +174.299i q^{4} +(596.761 + 596.761i) q^{5} +(590.820 + 590.820i) q^{6} -3526.08 q^{7} +(2750.23 + 2750.23i) q^{8} -1984.02 q^{9} +7628.33 q^{10} -10488.6i q^{11} -16112.1 q^{12} +(-17058.5 - 17058.5i) q^{13} +(-22536.8 + 22536.8i) q^{14} +(-55164.2 + 55164.2i) q^{15} -9464.66 q^{16} +(-29827.1 - 29827.1i) q^{17} +(-12680.7 + 12680.7i) q^{18} +(65980.9 + 65980.9i) q^{19} +(-104015. + 104015. i) q^{20} -325949. i q^{21} +(-67037.0 - 67037.0i) q^{22} +(331717. + 331717. i) q^{23} +(-254229. + 254229. i) q^{24} +321624. i q^{25} -218057. q^{26} +423093. i q^{27} -614593. i q^{28} +(-809690. + 809690. i) q^{29} +705157. i q^{30} +(917454. - 917454. i) q^{31} +(-764552. + 764552. i) q^{32} +969554. q^{33} -381276. q^{34} +(-2.10423e6 - 2.10423e6i) q^{35} -345812. i q^{36} +(-387928. - 1.83357e6i) q^{37} +843425. q^{38} +(1.57688e6 - 1.57688e6i) q^{39} +3.28246e6i q^{40} +3.95254e6i q^{41} +(-2.08328e6 - 2.08328e6i) q^{42} +(-2.11658e6 - 2.11658e6i) q^{43} +1.82814e6 q^{44} +(-1.18399e6 - 1.18399e6i) q^{45} +4.24031e6 q^{46} +2.44601e6 q^{47} -874906. i q^{48} +6.66847e6 q^{49} +(2.05564e6 + 2.05564e6i) q^{50} +(2.75719e6 - 2.75719e6i) q^{51} +(2.97328e6 - 2.97328e6i) q^{52} +2.90389e6 q^{53} +(2.70417e6 + 2.70417e6i) q^{54} +(6.25917e6 - 6.25917e6i) q^{55} +(-9.69755e6 - 9.69755e6i) q^{56} +(-6.09922e6 + 6.09922e6i) q^{57} +1.03502e7i q^{58} +(9.62403e6 + 9.62403e6i) q^{59} +(-9.61506e6 - 9.61506e6i) q^{60} +(-4.47557e6 + 4.47557e6i) q^{61} -1.17277e7i q^{62} +6.99582e6 q^{63} +7.35022e6i q^{64} -2.03597e7i q^{65} +(6.19685e6 - 6.19685e6i) q^{66} -7.55118e6i q^{67} +(5.19882e6 - 5.19882e6i) q^{68} +(-3.06637e7 + 3.06637e7i) q^{69} -2.68981e7 q^{70} +7.76602e6 q^{71} +(-5.45651e6 - 5.45651e6i) q^{72} +4.51232e7i q^{73} +(-1.41986e7 - 9.23976e6i) q^{74} -2.97306e7 q^{75} +(-1.15004e7 + 1.15004e7i) q^{76} +3.69835e7i q^{77} -2.01570e7i q^{78} +(3.90593e7 + 3.90593e7i) q^{79} +(-5.64814e6 - 5.64814e6i) q^{80} -5.21275e7 q^{81} +(2.52625e7 + 2.52625e7i) q^{82} +2.11151e7 q^{83} +5.68125e7 q^{84} -3.55993e7i q^{85} -2.70560e7 q^{86} +(-7.48472e7 - 7.48472e7i) q^{87} +(2.88459e7 - 2.88459e7i) q^{88} +(2.26682e7 - 2.26682e7i) q^{89} -1.51347e7 q^{90} +(6.01497e7 + 6.01497e7i) q^{91} +(-5.78180e7 + 5.78180e7i) q^{92} +(8.48087e7 + 8.48087e7i) q^{93} +(1.56335e7 - 1.56335e7i) q^{94} +7.87497e7i q^{95} +(-7.06746e7 - 7.06746e7i) q^{96} +(-1.06966e8 - 1.06966e8i) q^{97} +(4.26212e7 - 4.26212e7i) q^{98} +2.08095e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 4 q^{2} + 124 q^{5} + 510 q^{6} - 4 q^{7} - 5256 q^{8} - 93534 q^{9}+O(q^{10}) $ 50 * q + 4 * q^2 + 124 * q^5 + 510 * q^6 - 4 * q^7 - 5256 * q^8 - 93534 * q^9	\( 50 q + 4 q^{2} + 124 q^{5} + 510 q^{6} - 4 q^{7} - 5256 q^{8} - 93534 q^{9} - 10756 q^{10} - 45440 q^{12} + 63592 q^{13} - 80206 q^{14} - 124346 q^{15} - 639128 q^{16} - 178796 q^{17} - 45882 q^{18} + 264774 q^{19} + 469204 q^{20} + 714574 q^{22} - 654272 q^{23} - 1573644 q^{24} + 1841660 q^{26} - 1683686 q^{29} + 1766336 q^{31} - 4332632 q^{32} - 1438888 q^{33} - 5838452 q^{34} - 650482 q^{35} - 2870078 q^{37} - 2281528 q^{38} + 11036546 q^{39} - 7453902 q^{42} + 5097830 q^{43} - 14992464 q^{44} - 15078446 q^{45} + 28776464 q^{46} + 13992320 q^{47} + 4370314 q^{49} + 7603288 q^{50} + 19417938 q^{51} + 54318452 q^{52} + 28075952 q^{53} - 19197122 q^{54} - 6104306 q^{55} + 47803128 q^{56} + 17462426 q^{57} - 677072 q^{59} + 24953316 q^{60} + 4206386 q^{61} - 18098032 q^{63} - 56061730 q^{66} - 52579760 q^{68} + 88118984 q^{69} - 295493636 q^{70} - 37172476 q^{71} - 74582504 q^{72} - 224754524 q^{74} - 144364996 q^{75} + 189294548 q^{76} + 271163438 q^{79} - 312998084 q^{80} + 41535626 q^{81} - 177494710 q^{82} - 74250268 q^{83} - 82088924 q^{84} + 112964036 q^{86} - 142771908 q^{87} + 224951860 q^{88} + 84928780 q^{89} + 716592116 q^{90} - 40969098 q^{91} - 701292428 q^{92} - 83761576 q^{93} + 553881406 q^{94} - 7259376 q^{96} + 467792674 q^{97} + 538649310 q^{98}+O(q^{100}) \) 50 * q + 4 * q^2 + 124 * q^5 + 510 * q^6 - 4 * q^7 - 5256 * q^8 - 93534 * q^9 - 10756 * q^10 - 45440 * q^12 + 63592 * q^13 - 80206 * q^14 - 124346 * q^15 - 639128 * q^16 - 178796 * q^17 - 45882 * q^18 + 264774 * q^19 + 469204 * q^20 + 714574 * q^22 - 654272 * q^23 - 1573644 * q^24 + 1841660 * q^26 - 1683686 * q^29 + 1766336 * q^31 - 4332632 * q^32 - 1438888 * q^33 - 5838452 * q^34 - 650482 * q^35 - 2870078 * q^37 - 2281528 * q^38 + 11036546 * q^39 - 7453902 * q^42 + 5097830 * q^43 - 14992464 * q^44 - 15078446 * q^45 + 28776464 * q^46 + 13992320 * q^47 + 4370314 * q^49 + 7603288 * q^50 + 19417938 * q^51 + 54318452 * q^52 + 28075952 * q^53 - 19197122 * q^54 - 6104306 * q^55 + 47803128 * q^56 + 17462426 * q^57 - 677072 * q^59 + 24953316 * q^60 + 4206386 * q^61 - 18098032 * q^63 - 56061730 * q^66 - 52579760 * q^68 + 88118984 * q^69 - 295493636 * q^70 - 37172476 * q^71 - 74582504 * q^72 - 224754524 * q^74 - 144364996 * q^75 + 189294548 * q^76 + 271163438 * q^79 - 312998084 * q^80 + 41535626 * q^81 - 177494710 * q^82 - 74250268 * q^83 - 82088924 * q^84 + 112964036 * q^86 - 142771908 * q^87 + 224951860 * q^88 + 84928780 * q^89 + 716592116 * q^90 - 40969098 * q^91 - 701292428 * q^92 - 83761576 * q^93 + 553881406 * q^94 - 7259376 * q^96 + 467792674 * q^97 + 538649310 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	6.39144	−	6.39144i	0.399465	−	0.399465i	−0.478579	−	0.878044i	$-0.658848\pi$
$2$	6.39144	−	6.39144i	0.399465	−	0.399465i	0.878044	+	0.478579i	$0.158848\pi$
$3$			92.4393i			1.14123i	0.821219	+	0.570613i	$0.193294\pi$
$3$			92.4393i			1.14123i	−0.821219	+	0.570613i	$0.806706\pi$
$4$			174.299i			0.680855i
$5$	596.761	+	596.761i	0.954818	+	0.954818i	0.999023	−	0.0442041i	$-0.0140752\pi$
$5$	596.761	+	596.761i	0.954818	+	0.954818i	−0.0442041	+	0.999023i	$0.514075\pi$
$6$	590.820	+	590.820i	0.455880	+	0.455880i
$7$	−3526.08			−1.46859			−0.734295	−	0.678830i	$-0.762487\pi$
$7$	−3526.08			−1.46859			−0.734295	+	0.678830i	$0.762487\pi$
$8$	2750.23	+	2750.23i	0.671443	+	0.671443i
$9$	−1984.02			−0.302396
$10$	7628.33			0.762833
$11$		−	10488.6i		−	0.716382i	−0.933648	−	0.358191i	$-0.883394\pi$
$11$		−	10488.6i		−	0.716382i	0.933648	−	0.358191i	$-0.116606\pi$
$12$	−16112.1			−0.777009
$13$	−17058.5	−	17058.5i	−0.597266	−	0.597266i	0.342318	−	0.939584i	$-0.388788\pi$
$13$	−17058.5	−	17058.5i	−0.597266	−	0.597266i	−0.939584	+	0.342318i	$0.888788\pi$
$14$	−22536.8	+	22536.8i	−0.586650	+	0.586650i
$15$	−55164.2	+	55164.2i	−1.08966	+	1.08966i
$16$	−9464.66			−0.144419
$17$	−29827.1	−	29827.1i	−0.357120	−	0.357120i	0.505630	−	0.862750i	$-0.331260\pi$
$17$	−29827.1	−	29827.1i	−0.357120	−	0.357120i	−0.862750	+	0.505630i	$0.831260\pi$
$18$	−12680.7	+	12680.7i	−0.120797	+	0.120797i
$19$	65980.9	+	65980.9i	0.506295	+	0.506295i	0.913387	−	0.407092i	$-0.133457\pi$
$19$	65980.9	+	65980.9i	0.506295	+	0.506295i	−0.407092	+	0.913387i	$0.633457\pi$
$20$	−104015.	+	104015.i	−0.650093	+	0.650093i
$21$		−	325949.i		−	1.67599i
$22$	−67037.0	−	67037.0i	−0.286170	−	0.286170i
$23$	331717.	+	331717.i	1.18538	+	1.18538i	0.978331	+	0.207048i	$0.0663855\pi$
$23$	331717.	+	331717.i	1.18538	+	1.18538i	0.207048	+	0.978331i	$0.433614\pi$
$24$	−254229.	+	254229.i	−0.766268	+	0.766268i
$25$			321624.i			0.823356i
$26$	−218057.			−0.477174
$27$			423093.i			0.796124i
$28$		−	614593.i		−	0.999897i
$29$	−809690.	+	809690.i	−1.14479	+	1.14479i	−0.157231	+	0.987562i	$0.550257\pi$
$29$	−809690.	+	809690.i	−1.14479	+	1.14479i	−0.987562	+	0.157231i	$0.949743\pi$
$30$			705157.i			0.870565i
$31$	917454.	−	917454.i	0.993430	−	0.993430i	−0.00654851	−	0.999979i	$-0.502084\pi$
$31$	917454.	−	917454.i	0.993430	−	0.993430i	0.999979	+	0.00654851i	$0.00208447\pi$
$32$	−764552.	+	764552.i	−0.729133	+	0.729133i
$33$	969554.			0.817554
$34$	−381276.			−0.285314
$35$	−2.10423e6	−	2.10423e6i	−1.40224	−	1.40224i
$36$		−	345812.i		−	0.205888i
$37$	−387928.	−	1.83357e6i	−0.206988	−	0.978344i
$37$	−387928.	−	1.83357e6i	−0.206988	−	0.978344i
$38$	843425.			0.404494
$39$	1.57688e6	−	1.57688e6i	0.681615	−	0.681615i
$40$			3.28246e6i			1.28221i
$41$			3.95254e6i			1.39875i	0.714753	+	0.699377i	$0.246539\pi$
$41$			3.95254e6i			1.39875i	−0.714753	+	0.699377i	$0.753461\pi$
$42$	−2.08328e6	−	2.08328e6i	−0.669500	−	0.669500i
$43$	−2.11658e6	−	2.11658e6i	−0.619099	−	0.619099i	0.326201	−	0.945300i	$-0.394231\pi$
$43$	−2.11658e6	−	2.11658e6i	−0.619099	−	0.619099i	−0.945300	+	0.326201i	$0.894231\pi$
$44$	1.82814e6			0.487753
$45$	−1.18399e6	−	1.18399e6i	−0.288733	−	0.288733i
$46$	4.24031e6			0.947035
$47$	2.44601e6			0.501265			0.250632	−	0.968082i	$-0.419361\pi$
$47$	2.44601e6			0.501265			0.250632	+	0.968082i	$0.419361\pi$
$48$		−	874906.i		−	0.164815i
$49$	6.66847e6			1.15676
$50$	2.05564e6	+	2.05564e6i	0.328902	+	0.328902i
$51$	2.75719e6	−	2.75719e6i	0.407555	−	0.407555i
$52$	2.97328e6	−	2.97328e6i	0.406652	−	0.406652i
$53$	2.90389e6			0.368025			0.184012	−	0.982924i	$-0.441091\pi$
$53$	2.90389e6			0.368025			0.184012	+	0.982924i	$0.441091\pi$
$54$	2.70417e6	+	2.70417e6i	0.318024	+	0.318024i
$55$	6.25917e6	−	6.25917e6i	0.684015	−	0.684015i
$56$	−9.69755e6	−	9.69755e6i	−0.986075	−	0.986075i
$57$	−6.09922e6	+	6.09922e6i	−0.577797	+	0.577797i
$58$			1.03502e7i			0.914610i
$59$	9.62403e6	+	9.62403e6i	0.794235	+	0.794235i	0.982180	−	0.187945i	$-0.0601827\pi$
$59$	9.62403e6	+	9.62403e6i	0.794235	+	0.794235i	−0.187945	+	0.982180i	$0.560183\pi$
$60$	−9.61506e6	−	9.61506e6i	−0.741903	−	0.741903i
$61$	−4.47557e6	+	4.47557e6i	−0.323243	+	0.323243i	−0.850010	−	0.526767i	$-0.823404\pi$
$61$	−4.47557e6	+	4.47557e6i	−0.323243	+	0.323243i	0.526767	+	0.850010i	$0.323404\pi$
$62$		−	1.17277e7i		−	0.793681i
$63$	6.99582e6			0.444095
$64$			7.35022e6i			0.438107i
$65$		−	2.03597e7i		−	1.14056i
$66$	6.19685e6	−	6.19685e6i	0.326584	−	0.326584i
$67$		−	7.55118e6i		−	0.374728i	−0.982291	−	0.187364i	$-0.940006\pi$
$67$		−	7.55118e6i		−	0.374728i	0.982291	−	0.187364i	$-0.0599943\pi$
$68$	5.19882e6	−	5.19882e6i	0.243147	−	0.243147i
$69$	−3.06637e7	+	3.06637e7i	−1.35278	+	1.35278i
$70$	−2.68981e7			−1.12029
$71$	7.76602e6			0.305608			0.152804	−	0.988256i	$-0.451170\pi$
$71$	7.76602e6			0.305608			0.152804	+	0.988256i	$0.451170\pi$
$72$	−5.45651e6	−	5.45651e6i	−0.203041	−	0.203041i
$73$			4.51232e7i			1.58894i	0.607302	+	0.794471i	$0.292252\pi$
$73$			4.51232e7i			1.58894i	−0.607302	+	0.794471i	$0.707748\pi$
$74$	−1.41986e7	−	9.23976e6i	−0.473498	−	0.308130i
$75$	−2.97306e7			−0.939635
$76$	−1.15004e7	+	1.15004e7i	−0.344714	+	0.344714i
$77$			3.69835e7i			1.05207i
$78$		−	2.01570e7i		−	0.544563i
$79$	3.90593e7	+	3.90593e7i	1.00281	+	1.00281i	0.999996	+	0.00280897i	$0.000894125\pi$
$79$	3.90593e7	+	3.90593e7i	1.00281	+	1.00281i	0.00280897	+	0.999996i	$0.499106\pi$
$80$	−5.64814e6	−	5.64814e6i	−0.137894	−	0.137894i
$81$	−5.21275e7			−1.21095
$82$	2.52625e7	+	2.52625e7i	0.558753	+	0.558753i
$83$	2.11151e7			0.444919			0.222460	−	0.974942i	$-0.428591\pi$
$83$	2.11151e7			0.444919			0.222460	+	0.974942i	$0.428591\pi$
$84$	5.68125e7			1.14111
$85$		−	3.55993e7i		−	0.681970i
$86$	−2.70560e7			−0.494617
$87$	−7.48472e7	−	7.48472e7i	−1.30647	−	1.30647i
$88$	2.88459e7	−	2.88459e7i	0.481010	−	0.481010i
$89$	2.26682e7	−	2.26682e7i	0.361291	−	0.361291i	−0.502997	−	0.864288i	$-0.667769\pi$
$89$	2.26682e7	−	2.26682e7i	0.361291	−	0.361291i	0.864288	+	0.502997i	$0.167769\pi$
$90$	−1.51347e7			−0.230677
$91$	6.01497e7	+	6.01497e7i	0.877139	+	0.877139i
$92$	−5.78180e7	+	5.78180e7i	−0.807071	+	0.807071i
$93$	8.48087e7	+	8.48087e7i	1.13373	+	1.13373i
$94$	1.56335e7	−	1.56335e7i	0.200238	−	0.200238i
$95$			7.87497e7i			0.966839i
$96$	−7.06746e7	−	7.06746e7i	−0.832106	−	0.832106i
$97$	−1.06966e8	−	1.06966e8i	−1.20826	−	1.20826i	−0.971591	−	0.236667i	$-0.923945\pi$
$97$	−1.06966e8	−	1.06966e8i	−1.20826	−	1.20826i	−0.236667	−	0.971591i	$-0.576055\pi$
$98$	4.26212e7	−	4.26212e7i	0.462084	−	0.462084i
$99$			2.08095e7i			0.216631i
$100$	−5.60587e7			−0.560587
$101$			1.41280e8i			1.35768i	0.734288	+	0.678838i	$0.237516\pi$
$101$			1.41280e8i			1.35768i	−0.734288	+	0.678838i	$0.762484\pi$
$102$		−	3.52448e7i		−	0.325608i
$103$	9.27999e7	−	9.27999e7i	0.824515	−	0.824515i	−0.162237	−	0.986752i	$-0.551871\pi$
$103$	9.27999e7	−	9.27999e7i	0.824515	−	0.824515i	0.986752	+	0.162237i	$0.0518709\pi$
$104$		−	9.38297e7i		−	0.802060i
$105$	1.94514e8	−	1.94514e8i	1.60027	−	1.60027i
$106$	1.85601e7	−	1.85601e7i	0.147013	−	0.147013i
$107$	7.87599e7			0.600855			0.300428	−	0.953805i	$-0.402871\pi$
$107$	7.87599e7			0.600855			0.300428	+	0.953805i	$0.402871\pi$
$108$	−7.37446e7			−0.542045
$109$	2.03090e7	+	2.03090e7i	0.143874	+	0.143874i	0.775375	−	0.631501i	$-0.217561\pi$
$109$	2.03090e7	+	2.03090e7i	0.143874	+	0.143874i	−0.631501	+	0.775375i	$0.717561\pi$
$110$		−	8.00102e7i		−	0.546480i
$111$	1.69494e8	−	3.58598e7i	1.11651	−	0.236220i
$112$	3.33732e7			0.212093
$113$	2.57910e7	−	2.57910e7i	0.158181	−	0.158181i	−0.623579	−	0.781760i	$-0.714322\pi$
$113$	2.57910e7	−	2.57910e7i	0.158181	−	0.158181i	0.781760	+	0.623579i	$0.214322\pi$
$114$			7.79656e7i			0.461619i
$115$			3.95912e8i			2.26364i
$116$	−1.41128e8	−	1.41128e8i	−0.779439	−	0.779439i
$117$	3.38444e7	+	3.38444e7i	0.180611	+	0.180611i
$118$	1.23023e8			0.634538
$119$	1.05173e8	+	1.05173e8i	0.524464	+	0.524464i
$120$	−3.03429e8			−1.46329
$121$	1.04349e8			0.486796
$122$			5.72107e7i			0.258249i
$123$	−3.65370e8			−1.59629
$124$	1.59911e8	+	1.59911e8i	0.676382	+	0.676382i
$125$	4.11774e7	−	4.11774e7i	0.168663	−	0.168663i
$126$	4.47133e7	−	4.47133e7i	0.177401	−	0.177401i
$127$	−1.32603e8			−0.509728			−0.254864	−	0.966977i	$-0.582031\pi$
$127$	−1.32603e8			−0.509728			−0.254864	+	0.966977i	$0.582031\pi$
$128$	−1.48747e8	−	1.48747e8i	−0.554125	−	0.554125i
$129$	1.95655e8	−	1.95655e8i	0.706532	−	0.706532i
$130$	−1.30128e8	−	1.30128e8i	−0.455614	−	0.455614i
$131$	1.90381e8	−	1.90381e8i	0.646457	−	0.646457i	−0.305678	−	0.952135i	$-0.598883\pi$
$131$	1.90381e8	−	1.90381e8i	0.646457	−	0.646457i	0.952135	+	0.305678i	$0.0988832\pi$
$132$			1.68992e8i			0.556636i
$133$	−2.32654e8	−	2.32654e8i	−0.743540	−	0.743540i
$134$	−4.82629e7	−	4.82629e7i	−0.149691	−	0.149691i
$135$	−2.52486e8	+	2.52486e8i	−0.760154	+	0.760154i
$136$		−	1.64063e8i		−	0.479572i
$137$	1.42177e8			0.403597			0.201798	−	0.979427i	$-0.435321\pi$
$137$	1.42177e8			0.403597			0.201798	+	0.979427i	$0.435321\pi$
$138$			3.91971e8i			1.08078i
$139$		−	4.38028e8i		−	1.17339i	−0.809808	−	0.586695i	$-0.800429\pi$
$139$		−	4.38028e8i		−	1.17339i	0.809808	−	0.586695i	$-0.199571\pi$
$140$	3.66765e8	−	3.66765e8i	0.954720	−	0.954720i
$141$			2.26107e8i			0.572056i
$142$	4.96361e7	−	4.96361e7i	0.122080	−	0.122080i
$143$	−1.78919e8	+	1.78919e8i	−0.427871	+	0.427871i
$144$	1.87781e7			0.0436718
$145$	−9.66384e8			−2.18614
$146$	2.88402e8	+	2.88402e8i	0.634727	+	0.634727i
$147$			6.16429e8i			1.32012i
$148$	3.19590e8	−	6.76155e7i	0.666110	−	0.140929i
$149$	−4.88875e8			−0.991865			−0.495932	−	0.868361i	$-0.665174\pi$
$149$	−4.88875e8			−0.991865			−0.495932	+	0.868361i	$0.665174\pi$
$150$	−1.90022e8	+	1.90022e8i	−0.375351	+	0.375351i
$151$			7.08126e8i			1.36208i	0.732246	+	0.681041i	$0.238472\pi$
$151$			7.08126e8i			1.36208i	−0.732246	+	0.681041i	$0.761528\pi$
$152$			3.62925e8i			0.679896i
$153$	5.91774e7	+	5.91774e7i	0.107992	+	0.107992i
$154$	2.36378e8	+	2.36378e8i	0.420266	+	0.420266i
$155$	1.09500e9			1.89709
$156$	2.74848e8	+	2.74848e8i	0.464081	+	0.464081i
$157$	−2.37747e8			−0.391307			−0.195653	−	0.980673i	$-0.562683\pi$
$157$	−2.37747e8			−0.391307			−0.195653	+	0.980673i	$0.562683\pi$
$158$	4.99291e8			0.801171
$159$			2.68434e8i			0.419999i
$160$	−9.12510e8			−1.39238
$161$	−1.16966e9	−	1.16966e9i	−1.74084	−	1.74084i
$162$	−3.33170e8	+	3.33170e8i	−0.483733	+	0.483733i
$163$	3.31107e8	−	3.31107e8i	0.469049	−	0.469049i	−0.432557	−	0.901606i	$-0.642389\pi$
$163$	3.31107e8	−	3.31107e8i	0.469049	−	0.469049i	0.901606	+	0.432557i	$0.142389\pi$
$164$	−6.88924e8			−0.952349
$165$	5.78593e8	+	5.78593e8i	0.780616	+	0.780616i
$166$	1.34956e8	−	1.34956e8i	0.177730	−	0.177730i
$167$	7.82545e7	+	7.82545e7i	0.100611	+	0.100611i	0.755620	−	0.655010i	$-0.227336\pi$
$167$	7.82545e7	+	7.82545e7i	0.100611	+	0.100611i	−0.655010	+	0.755620i	$0.727336\pi$
$168$	8.96434e8	−	8.96434e8i	1.12533	−	1.12533i
$169$		−	2.33745e8i		−	0.286547i
$170$	−2.27531e8	−	2.27531e8i	−0.272423	−	0.272423i
$171$	−1.30907e8	−	1.30907e8i	−0.153101	−	0.153101i
$172$	3.68917e8	−	3.68917e8i	0.421517	−	0.421517i
$173$		−	1.22079e9i		−	1.36288i	−0.731874	−	0.681440i	$-0.761354\pi$
$173$		−	1.22079e9i		−	1.36288i	0.731874	−	0.681440i	$-0.238646\pi$
$174$	−9.56763e8			−1.04378
$175$		−	1.13407e9i		−	1.20917i
$176$			9.92706e7i			0.103459i
$177$	−8.89638e8	+	8.89638e8i	−0.906401	+	0.906401i
$178$		−	2.89765e8i		−	0.288646i
$179$	−1.26820e8	+	1.26820e8i	−0.123531	+	0.123531i	−0.766170	−	0.642638i	$-0.777840\pi$
$179$	−1.26820e8	+	1.26820e8i	−0.123531	+	0.123531i	0.642638	+	0.766170i	$0.277840\pi$
$180$	2.06367e8	−	2.06367e8i	0.196585	−	0.196585i
$181$	2.29404e8			0.213741			0.106870	−	0.994273i	$-0.465917\pi$
$181$	2.29404e8			0.213741			0.106870	+	0.994273i	$0.465917\pi$
$182$	7.68887e8			0.700772
$183$	−4.13719e8	−	4.13719e8i	−0.368893	−	0.368893i
$184$			1.82460e9i			1.59183i
$185$	8.62705e8	−	1.32571e9i	0.736505	−	1.13178i
$186$	1.08410e9			0.905769
$187$	−3.12843e8	+	3.12843e8i	−0.255835	+	0.255835i
$188$			4.26337e8i			0.341289i
$189$		−	1.49186e9i		−	1.16918i
$190$	5.03324e8	+	5.03324e8i	0.386219	+	0.386219i
$191$	7.69318e8	+	7.69318e8i	0.578060	+	0.578060i	0.934368	−	0.356309i	$-0.115965\pi$
$191$	7.69318e8	+	7.69318e8i	0.578060	+	0.578060i	−0.356309	+	0.934368i	$0.615965\pi$
$192$	−6.79449e8			−0.499979
$193$	4.04531e8	+	4.04531e8i	0.291556	+	0.291556i	0.837695	−	0.546139i	$-0.183903\pi$
$193$	4.04531e8	+	4.04531e8i	0.291556	+	0.291556i	−0.546139	+	0.837695i	$0.683903\pi$
$194$	−1.36734e9			−0.965313
$195$	1.88204e9			1.30164
$196$			1.16231e9i			0.787584i
$197$	2.06071e9			1.36821			0.684103	−	0.729386i	$-0.260194\pi$
$197$	2.06071e9			1.36821			0.684103	+	0.729386i	$0.260194\pi$
$198$	1.33003e8	+	1.33003e8i	0.0865365	+	0.0865365i
$199$	8.54844e8	−	8.54844e8i	0.545098	−	0.545098i	−0.379921	−	0.925019i	$-0.624049\pi$
$199$	8.54844e8	−	8.54844e8i	0.545098	−	0.545098i	0.925019	+	0.379921i	$0.124049\pi$
$200$	−8.84539e8	+	8.84539e8i	−0.552837	+	0.552837i
$201$	6.98026e8			0.427649
$202$	9.02985e8	+	9.02985e8i	0.542344	+	0.542344i
$203$	2.85504e9	−	2.85504e9i	1.68123	−	1.68123i
$204$	4.80576e8	+	4.80576e8i	0.277486	+	0.277486i
$205$	−2.35873e9	+	2.35873e9i	−1.33556	+	1.33556i
$206$		−	1.18625e9i		−	0.658730i
$207$	−6.58134e8	−	6.58134e8i	−0.358453	−	0.358453i
$208$	1.61453e8	+	1.61453e8i	0.0862567	+	0.0862567i
$209$	6.92044e8	−	6.92044e8i	0.362701	−	0.362701i
$210$		−	2.48644e9i		−	1.27850i
$211$	−3.13153e9			−1.57989			−0.789946	−	0.613176i	$-0.789891\pi$
$211$	−3.13153e9			−1.57989			−0.789946	+	0.613176i	$0.789891\pi$
$212$			5.06145e8i			0.250572i
$213$			7.17885e8i			0.348768i
$214$	5.03389e8	−	5.03389e8i	0.240021	−	0.240021i
$215$		−	2.52618e9i		−	1.18225i
$216$	−1.16360e9	+	1.16360e9i	−0.534552	+	0.534552i
$217$	−3.23502e9	+	3.23502e9i	−1.45894	+	1.45894i
$218$	2.59608e8			0.114946
$219$	−4.17115e9			−1.81334
$220$	1.09097e9	+	1.09097e9i	0.465715	+	0.465715i
$221$			1.01761e9i			0.426592i
$222$	8.54116e8	−	1.31251e9i	0.351646	−	0.540368i
$223$	−1.70907e9			−0.691100			−0.345550	−	0.938400i	$-0.612308\pi$
$223$	−1.70907e9			−0.691100			−0.345550	+	0.938400i	$0.612308\pi$
$224$	2.69587e9	−	2.69587e9i	1.07080	−	1.07080i
$225$		−	6.38107e8i		−	0.248979i
$226$		−	3.29683e8i		−	0.126376i
$227$	2.26630e9	+	2.26630e9i	0.853519	+	0.853519i	0.990565	−	0.137046i	$-0.0437607\pi$
$227$	2.26630e9	+	2.26630e9i	0.853519	+	0.853519i	−0.137046	+	0.990565i	$0.543761\pi$
$228$	−1.06309e9	−	1.06309e9i	−0.393396	−	0.393396i
$229$	1.78608e8			0.0649470			0.0324735	−	0.999473i	$-0.489662\pi$
$229$	1.78608e8			0.0649470			0.0324735	+	0.999473i	$0.489662\pi$
$230$	2.53045e9	+	2.53045e9i	0.904246	+	0.904246i
$231$	−3.41873e9			−1.20065
$232$	−4.45367e9			−1.53733
$233$			4.13346e9i			1.40246i	0.712935	+	0.701230i	$0.247365\pi$
$233$			4.13346e9i			1.40246i	−0.712935	+	0.701230i	$0.752635\pi$
$234$	4.32629e8			0.144295
$235$	1.45969e9	+	1.45969e9i	0.478617	+	0.478617i
$236$	−1.67746e9	+	1.67746e9i	−0.540759	+	0.540759i
$237$	−3.61062e9	+	3.61062e9i	−1.14443	+	1.14443i
$238$	1.34441e9			0.419010
$239$	−3.70406e9	−	3.70406e9i	−1.13524	−	1.13524i	−0.989293	−	0.145944i	$-0.953378\pi$
$239$	−3.70406e9	−	3.70406e9i	−1.13524	−	1.13524i	−0.145944	−	0.989293i	$-0.546622\pi$
$240$	5.22110e8	−	5.22110e8i	0.157368	−	0.157368i
$241$	−3.47659e9	−	3.47659e9i	−1.03059	−	1.03059i	−0.999517	−	0.0310716i	$-0.990108\pi$
$241$	−3.47659e9	−	3.47659e9i	−1.03059	−	1.03059i	−0.0310716	−	0.999517i	$-0.509892\pi$
$242$	6.66941e8	−	6.66941e8i	0.194458	−	0.194458i
$243$		−	2.04272e9i		−	0.585846i
$244$	−7.80088e8	−	7.80088e8i	−0.220082	−	0.220082i
$245$	3.97949e9	+	3.97949e9i	1.10449	+	1.10449i
$246$	−2.33524e9	+	2.33524e9i	−0.637664	+	0.637664i
$247$		−	2.25107e9i		−	0.604785i
$248$	5.04642e9			1.33406
$249$			1.95187e9i			0.507753i
$250$		−	5.26366e8i		−	0.134750i
$251$	−1.42345e8	+	1.42345e8i	−0.0358630	+	0.0358630i	−0.724811	−	0.688948i	$-0.758073\pi$
$251$	−1.42345e8	+	1.42345e8i	−0.0358630	+	0.0358630i	0.688948	+	0.724811i	$0.258073\pi$
$252$			1.21936e9i			0.302365i
$253$	3.47924e9	−	3.47924e9i	0.849184	−	0.849184i
$254$	−8.47525e8	+	8.47525e8i	−0.203619	+	0.203619i
$255$	3.29077e9			0.778282
$256$	−3.78307e9			−0.880814
$257$	−3.55075e9	−	3.55075e9i	−0.813930	−	0.813930i	0.171290	−	0.985221i	$-0.445206\pi$
$257$	−3.55075e9	−	3.55075e9i	−0.813930	−	0.813930i	−0.985221	+	0.171290i	$0.945206\pi$
$258$		−	2.50103e9i		−	0.564470i
$259$	1.36787e9	+	6.46534e9i	0.303980	+	1.43679i
$260$	3.54868e9			0.776557
$261$	1.60644e9	−	1.60644e9i	0.346181	−	0.346181i
$262$		−	2.43362e9i		−	0.516474i
$263$		−	2.47191e9i		−	0.516665i	−0.966056	−	0.258333i	$-0.916827\pi$
$263$		−	2.47191e9i		−	0.516665i	0.966056	−	0.258333i	$-0.0831730\pi$
$264$	2.66650e9	+	2.66650e9i	0.548941	+	0.548941i
$265$	1.73293e9	+	1.73293e9i	0.351397	+	0.351397i
$266$	−2.97399e9			−0.594036
$267$	2.09543e9	+	2.09543e9i	0.412315	+	0.412315i
$268$	1.31616e9			0.255135
$269$	8.02992e9			1.53356			0.766782	−	0.641907i	$-0.221856\pi$
$269$	8.02992e9			1.53356			0.766782	+	0.641907i	$0.221856\pi$
$270$			3.22749e9i			0.607310i
$271$	2.03565e9			0.377422			0.188711	−	0.982033i	$-0.439569\pi$
$271$	2.03565e9			0.377422			0.188711	+	0.982033i	$0.439569\pi$
$272$	2.82303e8	+	2.82303e8i	0.0515751	+	0.0515751i
$273$	−5.56020e9	+	5.56020e9i	−1.00101	+	1.00101i
$274$	9.08717e8	−	9.08717e8i	0.161223	−	0.161223i
$275$	3.37337e9			0.589838
$276$	−5.34465e9	−	5.34465e9i	−0.921050	−	0.921050i
$277$	−2.20329e9	+	2.20329e9i	−0.374241	+	0.374241i	−0.869019	−	0.494778i	$-0.835249\pi$
$277$	−2.20329e9	+	2.20329e9i	−0.374241	+	0.374241i	0.494778	+	0.869019i	$0.335249\pi$
$278$	−2.79963e9	−	2.79963e9i	−0.468728	−	0.468728i
$279$	−1.82024e9	+	1.82024e9i	−0.300409	+	0.300409i
$280$		−	1.15742e10i		−	1.88304i
$281$	4.89179e9	+	4.89179e9i	0.784589	+	0.784589i	0.980601	−	0.196012i	$-0.0627993\pi$
$281$	4.89179e9	+	4.89179e9i	0.784589	+	0.784589i	−0.196012	+	0.980601i	$0.562799\pi$
$282$	1.44515e9	+	1.44515e9i	0.228516	+	0.228516i
$283$	7.53879e9	−	7.53879e9i	1.17532	−	1.17532i	0.194396	−	0.980923i	$-0.437725\pi$
$283$	7.53879e9	−	7.53879e9i	1.17532	−	1.17532i	0.980923	−	0.194396i	$-0.0622746\pi$
$284$			1.35361e9i			0.208075i
$285$	−7.27956e9			−1.10338
$286$			2.28710e9i			0.341839i
$287$		−	1.39370e10i		−	2.05420i
$288$	1.51688e9	−	1.51688e9i	0.220487	−	0.220487i
$289$		−	5.19645e9i		−	0.744930i
$290$	−6.17659e9	+	6.17659e9i	−0.873286	+	0.873286i
$291$	9.88787e9	−	9.88787e9i	1.37889	−	1.37889i
$292$	−7.86492e9			−1.08184
$293$	1.67259e9			0.226945			0.113472	−	0.993541i	$-0.463803\pi$
$293$	1.67259e9			0.226945			0.113472	+	0.993541i	$0.463803\pi$
$294$	3.93987e9	+	3.93987e9i	0.527342	+	0.527342i
$295$			1.14865e10i			1.51670i
$296$	3.97586e9	−	6.10964e9i	0.517922	−	0.795882i
$297$	4.43763e9			0.570329
$298$	−3.12461e9	+	3.12461e9i	−0.396215	+	0.396215i
$299$		−	1.13172e10i		−	1.41597i
$300$		−	5.18202e9i		−	0.639756i
$301$	7.46323e9	+	7.46323e9i	0.909203	+	0.909203i
$302$	4.52595e9	+	4.52595e9i	0.544104	+	0.544104i
$303$	−1.30599e10			−1.54942
$304$	−6.24486e8	−	6.24486e8i	−0.0731187	−	0.0731187i
$305$	−5.34170e9			−0.617277
$306$	7.56458e8			0.0862778
$307$		−	4.58829e9i		−	0.516532i	−0.966074	−	0.258266i	$-0.916849\pi$
$307$		−	4.58829e9i		−	0.516532i	0.966074	−	0.258266i	$-0.0831511\pi$
$308$	−6.44619e9			−0.716309
$309$	8.57835e9	+	8.57835e9i	0.940957	+	0.940957i
$310$	6.99864e9	−	6.99864e9i	0.757821	−	0.757821i
$311$	−1.21060e10	+	1.21060e10i	−1.29407	+	1.29407i	−0.361822	+	0.932247i	$0.617845\pi$
$311$	−1.21060e10	+	1.21060e10i	−1.29407	+	1.29407i	−0.932247	+	0.361822i	$0.882155\pi$
$312$	8.67354e9			0.915331
$313$	−7.00974e9	−	7.00974e9i	−0.730339	−	0.730339i	0.240348	−	0.970687i	$-0.422738\pi$
$313$	−7.00974e9	−	7.00974e9i	−0.730339	−	0.730339i	−0.970687	+	0.240348i	$0.922738\pi$
$314$	−1.51955e9	+	1.51955e9i	−0.156313	+	0.156313i
$315$	4.17483e9	+	4.17483e9i	0.424030	+	0.424030i
$316$	−6.80800e9	+	6.80800e9i	−0.682765	+	0.682765i
$317$		−	1.52676e8i		−	0.0151194i	−0.999971	−	0.00755968i	$-0.997594\pi$
$317$		−	1.52676e8i		−	0.0151194i	0.999971	−	0.00755968i	$-0.00240634\pi$
$318$	1.71568e9	+	1.71568e9i	0.167775	+	0.167775i
$319$	8.49248e9	+	8.49248e9i	0.820110	+	0.820110i
$320$	−4.38633e9	+	4.38633e9i	−0.418313	+	0.418313i
$321$			7.28050e9i			0.685711i
$322$	−1.49517e10			−1.39081
$323$		−	3.93603e9i		−	0.361616i
$324$		−	9.08578e9i		−	0.824483i
$325$	5.48642e9	−	5.48642e9i	0.491763	−	0.491763i
$326$		−	4.23251e9i		−	0.374738i
$327$	−1.87735e9	+	1.87735e9i	−0.164193	+	0.164193i
$328$	−1.08704e10	+	1.08704e10i	−0.939184	+	0.939184i
$329$	−8.62484e9			−0.736152
$330$	7.39608e9			0.623657
$331$	9.79570e9	+	9.79570e9i	0.816063	+	0.816063i	0.985535	−	0.169472i	$-0.0542063\pi$
$331$	9.79570e9	+	9.79570e9i	0.816063	+	0.816063i	−0.169472	+	0.985535i	$0.554206\pi$
$332$			3.68034e9i			0.302926i
$333$	7.69656e8	+	3.63784e9i	0.0625922	+	0.295847i
$334$	1.00032e9			0.0803808
$335$	4.50626e9	−	4.50626e9i	0.357797	−	0.357797i
$336$			3.08499e9i			0.242046i
$337$			1.32594e10i			1.02803i	0.857782	+	0.514014i	$0.171842\pi$
$337$			1.32594e10i			1.02803i	−0.857782	+	0.514014i	$0.828158\pi$
$338$	−1.49397e9	−	1.49397e9i	−0.114466	−	0.114466i
$339$	2.38410e9	+	2.38410e9i	0.180520	+	0.180520i
$340$	6.20492e9			0.464323
$341$	−9.62276e9	−	9.62276e9i	−0.711676	−	0.711676i
$342$	−1.67337e9			−0.122317
$343$	−3.18643e9			−0.230212
$344$		−	1.16422e10i		−	0.831380i
$345$	−3.65979e10			−2.58333
$346$	−7.80263e9	−	7.80263e9i	−0.544423	−	0.544423i
$347$	1.76675e10	−	1.76675e10i	1.21859	−	1.21859i	0.250466	−	0.968125i	$-0.419416\pi$
$347$	1.76675e10	−	1.76675e10i	1.21859	−	1.21859i	0.968125	−	0.250466i	$-0.0805838\pi$
$348$	1.30458e10	−	1.30458e10i	0.889515	−	0.889515i
$349$	7.32195e9			0.493543			0.246772	−	0.969074i	$-0.420630\pi$
$349$	7.32195e9			0.493543			0.246772	+	0.969074i	$0.420630\pi$
$350$	−7.24835e9	−	7.24835e9i	−0.483022	−	0.483022i
$351$	7.21733e9	−	7.21733e9i	0.475498	−	0.475498i
$352$	8.01904e9	+	8.01904e9i	0.522338	+	0.522338i
$353$	−1.20095e10	+	1.20095e10i	−0.773442	+	0.773442i	−0.978707	−	0.205265i	$-0.934194\pi$
$353$	−1.20095e10	+	1.20095e10i	−0.773442	+	0.773442i	0.205265	+	0.978707i	$0.434194\pi$
$354$			1.13721e10i			0.724151i
$355$	4.63446e9	+	4.63446e9i	0.291800	+	0.291800i
$356$	3.95105e9	+	3.95105e9i	0.245987	+	0.245987i
$357$	−9.72209e9	+	9.72209e9i	−0.598531	+	0.598531i
$358$			1.62113e9i			0.0986928i
$359$	1.31642e10			0.792531			0.396265	−	0.918136i	$-0.370306\pi$
$359$	1.31642e10			0.792531			0.396265	+	0.918136i	$0.370306\pi$
$360$		−	6.51247e9i		−	0.387735i
$361$		−	8.27662e9i		−	0.487331i
$362$	1.46622e9	−	1.46622e9i	0.0853820	−	0.0853820i
$363$			9.64595e9i			0.555544i
$364$	−1.04840e10	+	1.04840e10i	−0.597204	+	0.597204i
$365$	−2.69278e10	+	2.69278e10i	−1.51715	+	1.51715i
$366$	−5.28852e9			−0.294720
$367$	8.25711e9			0.455160			0.227580	−	0.973759i	$-0.426919\pi$
$367$	8.25711e9			0.455160			0.227580	+	0.973759i	$0.426919\pi$
$368$	−3.13959e9	−	3.13959e9i	−0.171191	−	0.171191i
$369$		−	7.84192e9i		−	0.422977i
$370$	−2.95924e9	−	1.39871e10i	−0.157897	−	0.746313i
$371$	−1.02394e10			−0.540477
$372$	−1.47821e10	+	1.47821e10i	−0.771905	+	0.771905i
$373$		−	1.74469e10i		−	0.901328i	−0.892694	−	0.450664i	$-0.851187\pi$
$373$		−	1.74469e10i		−	0.901328i	0.892694	−	0.450664i	$-0.148813\pi$
$374$			3.99903e9i			0.204394i
$375$	3.80641e9	+	3.80641e9i	0.192482	+	0.192482i
$376$	6.72709e9	+	6.72709e9i	0.336571	+	0.336571i
$377$	2.76242e10			1.36749
$378$	−9.53514e9	−	9.53514e9i	−0.467046	−	0.467046i
$379$	2.68401e10			1.30085			0.650424	−	0.759571i	$-0.274591\pi$
$379$	2.68401e10			1.30085			0.650424	+	0.759571i	$0.274591\pi$
$380$	−1.37260e10			−0.658278
$381$		−	1.22577e10i		−	0.581715i
$382$	9.83410e9			0.461829
$383$	−1.78435e9	−	1.78435e9i	−0.0829250	−	0.0829250i	0.664428	−	0.747353i	$-0.268675\pi$
$383$	−1.78435e9	−	1.78435e9i	−0.0829250	−	0.0829250i	−0.747353	+	0.664428i	$0.768675\pi$
$384$	1.37500e10	−	1.37500e10i	0.632381	−	0.632381i
$385$	−2.20704e10	+	2.20704e10i	−1.00454	+	1.00454i
$386$	5.17107e9			0.232933
$387$	4.19933e9	+	4.19933e9i	0.187213	+	0.187213i
$388$	1.86441e10	−	1.86441e10i	0.822649	−	0.822649i
$389$	−5.69670e8	−	5.69670e8i	−0.0248785	−	0.0248785i	0.694558	−	0.719437i	$-0.255600\pi$
$389$	−5.69670e8	−	5.69670e8i	−0.0248785	−	0.0248785i	−0.719437	+	0.694558i	$0.755600\pi$
$390$	1.20289e10	−	1.20289e10i	0.519959	−	0.519959i
$391$		−	1.97883e10i		−	0.846646i
$392$	1.83398e10	+	1.83398e10i	0.776696	+	0.776696i
$393$	1.75987e10	+	1.75987e10i	0.737753	+	0.737753i
$394$	1.31709e10	−	1.31709e10i	0.546550	−	0.546550i
$395$			4.66182e10i			1.91499i
$396$	−3.62707e9			−0.147494
$397$		−	8.67913e9i		−	0.349393i	−0.984622	−	0.174696i	$-0.944106\pi$
$397$		−	8.67913e9i		−	0.349393i	0.984622	−	0.174696i	$-0.0558944\pi$
$398$		−	1.09274e10i		−	0.435495i
$399$	2.15064e10	−	2.15064e10i	0.848546	−	0.848546i
$400$		−	3.04406e9i		−	0.118908i
$401$	3.11852e10	−	3.11852e10i	1.20606	−	1.20606i	0.233773	−	0.972291i	$-0.424893\pi$
$401$	3.11852e10	−	3.11852e10i	1.20606	−	1.20606i	0.972291	−	0.233773i	$-0.0751074\pi$
$402$	4.46139e9	−	4.46139e9i	0.170831	−	0.170831i
$403$	−3.13008e10			−1.18668
$404$	−2.46250e10			−0.924381
$405$	−3.11077e10	−	3.11077e10i	−1.15624	−	1.15624i
$406$		−	3.64956e10i		−	1.34319i
$407$	−1.92315e10	+	4.06881e9i	−0.700868	+	0.148282i
$408$	1.51658e10			0.547300
$409$	−2.45694e10	+	2.45694e10i	−0.878015	+	0.878015i	−0.993329	−	0.115314i	$-0.963212\pi$
$409$	−2.45694e10	+	2.45694e10i	−0.878015	+	0.878015i	0.115314	+	0.993329i	$0.463212\pi$
$410$			3.01513e10i			1.06702i
$411$			1.31427e10i			0.460595i
$412$	1.61749e10	+	1.61749e10i	0.561375	+	0.561375i
$413$	−3.39351e10	−	3.39351e10i	−1.16640	−	1.16640i
$414$	−8.41284e9			−0.286379
$415$	1.26007e10	+	1.26007e10i	0.424817	+	0.424817i
$416$	2.60842e10			0.870973
$417$	4.04910e10			1.33910
$418$		−	8.84632e9i		−	0.289773i
$419$	−4.08732e10			−1.32612			−0.663060	−	0.748566i	$-0.730743\pi$
$419$	−4.08732e10			−1.32612			−0.663060	+	0.748566i	$0.730743\pi$
$420$	3.39035e10	+	3.39035e10i	1.08955	+	1.08955i
$421$	3.75975e10	−	3.75975e10i	1.19682	−	1.19682i	0.221713	−	0.975112i	$-0.428835\pi$
$421$	3.75975e10	−	3.75975e10i	1.19682	−	1.19682i	0.975112	−	0.221713i	$-0.0711648\pi$
$422$	−2.00150e10	+	2.00150e10i	−0.631112	+	0.631112i
$423$	−4.85293e9			−0.151580
$424$	7.98637e9	+	7.98637e9i	0.247108	+	0.247108i
$425$	9.59308e9	−	9.59308e9i	0.294037	−	0.294037i
$426$	4.58832e9	+	4.58832e9i	0.139321	+	0.139321i
$427$	1.57813e10	−	1.57813e10i	0.474712	−	0.474712i
$428$			1.37278e10i			0.409095i
$429$	−1.65392e10	−	1.65392e10i	−0.488297	−	0.488297i
$430$	−1.61460e10	−	1.61460e10i	−0.472270	−	0.472270i
$431$	−4.04399e9	+	4.04399e9i	−0.117193	+	0.117193i	−0.763271	−	0.646078i	$-0.776408\pi$
$431$	−4.04399e9	+	4.04399e9i	−0.117193	+	0.117193i	0.646078	+	0.763271i	$0.276408\pi$
$432$		−	4.00443e9i		−	0.114976i
$433$	−4.98044e10			−1.41682			−0.708412	−	0.705799i	$-0.750588\pi$
$433$	−4.98044e10			−1.41682			−0.708412	+	0.705799i	$0.750588\pi$
$434$			4.13529e10i			1.16559i
$435$		−	8.93318e10i		−	2.49488i
$436$	−3.53985e9	+	3.53985e9i	−0.0979577	+	0.0979577i
$437$			4.37740e10i			1.20030i
$438$	−2.66597e10	+	2.66597e10i	−0.724367	+	0.724367i
$439$	3.08611e10	−	3.08611e10i	0.830909	−	0.830909i	−0.156732	−	0.987641i	$-0.550096\pi$
$439$	3.08611e10	−	3.08611e10i	0.830909	−	0.830909i	0.987641	+	0.156732i	$0.0500960\pi$
$440$	3.44283e10			0.918554
$441$	−1.32304e10			−0.349798
$442$	6.50400e9	+	6.50400e9i	0.170408	+	0.170408i
$443$			5.20571e10i			1.35165i	0.737061	+	0.675826i	$0.236213\pi$
$443$			5.20571e10i			1.35165i	−0.737061	+	0.675826i	$0.763787\pi$
$444$	6.25032e9	+	2.95427e10i	0.160831	+	0.760182i
$445$	2.70550e10			0.689935
$446$	−1.09234e10	+	1.09234e10i	−0.276070	+	0.276070i
$447$		−	4.51912e10i		−	1.13194i
$448$		−	2.59175e10i		−	0.643400i
$449$	6.61517e9	+	6.61517e9i	0.162763	+	0.162763i	0.783790	−	0.621026i	$-0.213284\pi$
$449$	6.61517e9	+	6.61517e9i	0.162763	+	0.162763i	−0.621026	+	0.783790i	$0.713284\pi$
$450$	−4.07842e9	−	4.07842e9i	−0.0994586	−	0.0994586i
$451$	4.14565e10			1.00204
$452$	4.49534e9	+	4.49534e9i	0.107698	+	0.107698i
$453$	−6.54587e10			−1.55444
$454$	2.89698e10			0.681902
$455$			7.17901e10i			1.67502i
$456$	−3.35485e10			−0.775915
$457$	−2.56745e10	−	2.56745e10i	−0.588622	−	0.588622i	0.348636	−	0.937258i	$-0.386645\pi$
$457$	−2.56745e10	−	2.56745e10i	−0.588622	−	0.588622i	−0.937258	+	0.348636i	$0.886645\pi$
$458$	1.14156e9	−	1.14156e9i	0.0259441	−	0.0259441i
$459$	1.26196e10	−	1.26196e10i	0.284312	−	0.284312i
$460$	−6.90071e10			−1.54121
$461$	−2.06844e10	−	2.06844e10i	−0.457973	−	0.457973i	0.440017	−	0.897990i	$-0.354972\pi$
$461$	−2.06844e10	−	2.06844e10i	−0.457973	−	0.457973i	−0.897990	+	0.440017i	$0.854972\pi$
$462$	−2.18506e10	+	2.18506e10i	−0.479618	+	0.479618i
$463$	4.08534e10	+	4.08534e10i	0.889005	+	0.889005i	0.994428	−	0.105423i	$-0.0336195\pi$
$463$	4.08534e10	+	4.08534e10i	0.889005	+	0.889005i	−0.105423	+	0.994428i	$0.533620\pi$
$464$	7.66344e9	−	7.66344e9i	0.165330	−	0.165330i
$465$			1.01221e11i			2.16501i
$466$	2.64188e10	+	2.64188e10i	0.560234	+	0.560234i
$467$	−6.06012e10	−	6.06012e10i	−1.27413	−	1.27413i	−0.943901	−	0.330227i	$-0.892875\pi$
$467$	−6.06012e10	−	6.06012e10i	−1.27413	−	1.27413i	−0.330227	−	0.943901i	$-0.607125\pi$
$468$	−5.89904e9	+	5.89904e9i	−0.122970	+	0.122970i
$469$			2.66261e10i			0.550321i
$470$	1.86590e10			0.382381
$471$		−	2.19772e10i		−	0.446569i
$472$			5.29366e10i			1.06657i
$473$	−2.21998e10	+	2.21998e10i	−0.443512	+	0.443512i
$474$			4.61541e10i			0.914317i
$475$	−2.12210e10	+	2.12210e10i	−0.416861	+	0.416861i
$476$	−1.83315e10	+	1.83315e10i	−0.357084	+	0.357084i
$477$	−5.76137e9			−0.111289
$478$	−4.73486e10			−0.906975
$479$	2.14855e10	+	2.14855e10i	0.408134	+	0.408134i	0.881088	−	0.472953i	$-0.156812\pi$
$479$	2.14855e10	+	2.14855e10i	0.408134	+	0.408134i	−0.472953	+	0.881088i	$0.656812\pi$
$480$		−	8.43518e10i		−	1.58902i
$481$	−2.46606e10	+	3.78955e10i	−0.460705	+	0.707958i
$482$	−4.44409e10			−0.823368
$483$	1.08123e11	−	1.08123e11i	1.98669	−	1.98669i
$484$			1.81879e10i			0.331438i
$485$		−	1.27667e11i		−	2.30733i
$486$	−1.30559e10	−	1.30559e10i	−0.234025	−	0.234025i
$487$	−5.14899e10	−	5.14899e10i	−0.915391	−	0.915391i	0.0812991	−	0.996690i	$-0.474093\pi$
$487$	−5.14899e10	−	5.14899e10i	−0.915391	−	0.915391i	−0.996690	+	0.0812991i	$0.974093\pi$
$488$	−2.46177e10			−0.434079
$489$	3.06073e10	+	3.06073e10i	0.535291	+	0.535291i
$490$	5.08693e10			0.882413
$491$	6.97259e9			0.119969			0.0599844	−	0.998199i	$-0.480895\pi$
$491$	6.97259e9			0.119969			0.0599844	+	0.998199i	$0.480895\pi$
$492$		−	6.36837e10i		−	1.08685i
$493$	4.83014e10			0.817658
$494$	−1.43876e10	−	1.43876e10i	−0.241591	−	0.241591i
$495$	−1.24183e10	+	1.24183e10i	−0.206843	+	0.206843i
$496$	−8.68338e9	+	8.68338e9i	−0.143470	+	0.143470i
$497$	−2.73836e10			−0.448813
$498$	1.24752e10	+	1.24752e10i	0.202830	+	0.202830i
$499$	−4.17389e10	+	4.17389e10i	−0.673191	+	0.673191i	−0.958450	−	0.285259i	$-0.907920\pi$
$499$	−4.17389e10	+	4.17389e10i	−0.673191	+	0.673191i	0.285259	+	0.958450i	$0.407920\pi$
$500$	7.17718e9	+	7.17718e9i	0.114835	+	0.114835i
$501$	−7.23379e9	+	7.23379e9i	−0.114819	+	0.114819i
$502$			1.81958e9i			0.0286521i
$503$	−3.82498e10	−	3.82498e10i	−0.597526	−	0.597526i	0.342127	−	0.939654i	$-0.388853\pi$
$503$	−3.82498e10	−	3.82498e10i	−0.597526	−	0.597526i	−0.939654	+	0.342127i	$0.888853\pi$
$504$	1.92401e10	+	1.92401e10i	0.298185	+	0.298185i
$505$	−8.43107e10	+	8.43107e10i	−1.29633	+	1.29633i
$506$		−	4.44747e10i		−	0.678439i
$507$	2.16072e10			0.327015
$508$		−	2.31126e10i		−	0.347051i
$509$			9.69282e10i			1.44404i	0.691872	+	0.722020i	$0.256786\pi$
$509$			9.69282e10i			1.44404i	−0.691872	+	0.722020i	$0.743214\pi$
$510$	2.10328e10	−	2.10328e10i	0.310896	−	0.310896i
$511$		−	1.59108e11i		−	2.33351i
$512$	1.38999e10	−	1.38999e10i	0.202270	−	0.202270i
$513$	−2.79160e10	+	2.79160e10i	−0.403073	+	0.403073i
$514$	−4.53888e10			−0.650273
$515$	1.10759e11			1.57452
$516$	3.41024e10	+	3.41024e10i	0.481046	+	0.481046i
$517$		−	2.56551e10i		−	0.359097i
$518$	5.00655e10	+	3.25802e10i	0.695375	+	0.452516i
$519$	1.12849e11			1.55535
$520$	5.59939e10	−	5.59939e10i	0.765821	−	0.765821i
$521$			2.06434e10i			0.280176i	0.990139	+	0.140088i	$0.0447385\pi$
$521$			2.06434e10i			0.280176i	−0.990139	+	0.140088i	$0.955262\pi$
$522$		−	2.05349e10i		−	0.276574i
$523$	4.93782e9	+	4.93782e9i	0.0659976	+	0.0659976i	0.739335	−	0.673338i	$-0.235140\pi$
$523$	4.93782e9	+	4.93782e9i	0.0659976	+	0.0659976i	−0.673338	+	0.739335i	$0.735140\pi$
$524$	3.31833e10	+	3.31833e10i	0.440143	+	0.440143i
$525$	1.04833e11			1.37994
$526$	−1.57990e10	−	1.57990e10i	−0.206390	−	0.206390i
$527$	−5.47299e10			−0.709548
$528$	−9.17650e9			−0.118071
$529$			1.41762e11i			1.81024i
$530$	2.21519e10			0.280741
$531$	−1.90942e10	−	1.90942e10i	−0.240173	−	0.240173i
$532$	4.05514e10	−	4.05514e10i	0.506243	−	0.506243i
$533$	6.74245e10	−	6.74245e10i	0.835428	−	0.835428i
$534$	2.67857e10			0.329411
$535$	4.70008e10	+	4.70008e10i	0.573708	+	0.573708i
$536$	2.07675e10	−	2.07675e10i	0.251608	−	0.251608i
$537$	−1.17232e10	−	1.17232e10i	−0.140977	−	0.140977i
$538$	5.13228e10	−	5.13228e10i	0.612606	−	0.612606i
$539$		−	6.99427e10i		−	0.828680i
$540$	−4.40080e10	−	4.40080e10i	−0.517555	−	0.517555i
$541$	5.04110e10	+	5.04110e10i	0.588486	+	0.588486i	0.937221	−	0.348735i	$-0.113389\pi$
$541$	5.04110e10	+	5.04110e10i	0.588486	+	0.588486i	−0.348735	+	0.937221i	$0.613389\pi$
$542$	1.30108e10	−	1.30108e10i	0.150767	−	0.150767i
$543$			2.12060e10i			0.243926i
$544$	4.56087e10			0.520777
$545$			2.42393e10i			0.274748i
$546$			7.10754e10i			0.799739i
$547$	−9.41613e10	+	9.41613e10i	−1.05178	+	1.05178i	−0.0531912	+	0.998584i	$0.516939\pi$
$547$	−9.41613e10	+	9.41613e10i	−1.05178	+	1.05178i	−0.998584	+	0.0531912i	$0.983061\pi$
$548$			2.47813e10i			0.274791i
$549$	8.87962e9	−	8.87962e9i	0.0977473	−	0.0977473i
$550$	2.15607e10	−	2.15607e10i	0.235620	−	0.235620i
$551$	−1.06848e11			−1.15921
$552$	−1.68665e11			−1.81663
$553$	−1.37727e11	−	1.37727e11i	−1.47271	−	1.47271i
$554$			2.81644e10i			0.298993i
$555$	1.22547e11	+	7.97479e10i	1.29161	+	0.840518i
$556$	7.63478e10			0.798909
$557$	7.39318e10	−	7.39318e10i	0.768087	−	0.768087i	−0.209682	−	0.977770i	$-0.567243\pi$
$557$	7.39318e10	−	7.39318e10i	0.768087	−	0.768087i	0.977770	+	0.209682i	$0.0672430\pi$
$558$			2.32680e10i			0.240006i
$559$			7.22113e10i			0.739534i
$560$	1.99158e10	+	1.99158e10i	0.202510	+	0.202510i
$561$	−2.89190e10	−	2.89190e10i	−0.291965	−	0.291965i
$562$	6.25311e10			0.626832
$563$	−1.21840e11	−	1.21840e11i	−1.21271	−	1.21271i	−0.970131	−	0.242581i	$-0.922006\pi$
$563$	−1.21840e11	−	1.21840e11i	−1.21271	−	1.21271i	−0.242581	−	0.970131i	$-0.577994\pi$
$564$	−3.94103e10			−0.389487
$565$	3.07821e10			0.302068
$566$		−	9.63674e10i		−	0.938998i
$567$	1.83806e11			1.77839
$568$	2.13583e10	+	2.13583e10i	0.205199	+	0.205199i
$569$	−1.68613e10	+	1.68613e10i	−0.160858	+	0.160858i	−0.782947	−	0.622089i	$-0.786284\pi$
$569$	−1.68613e10	+	1.68613e10i	−0.160858	+	0.160858i	0.622089	+	0.782947i	$0.286284\pi$
$570$	−4.65269e10	+	4.65269e10i	−0.440762	+	0.440762i
$571$	−7.79024e10			−0.732835			−0.366417	−	0.930451i	$-0.619416\pi$
$571$	−7.79024e10			−0.732835			−0.366417	+	0.930451i	$0.619416\pi$
$572$	−3.11854e10	−	3.11854e10i	−0.291318	−	0.291318i
$573$	−7.11152e10	+	7.11152e10i	−0.659696	+	0.659696i
$574$	−8.90776e10	−	8.90776e10i	−0.820580	−	0.820580i
$575$	−1.06688e11	+	1.06688e11i	−0.975989	+	0.975989i
$576$		−	1.45830e10i		−	0.132482i
$577$	−1.28512e11	−	1.28512e11i	−1.15942	−	1.15942i	−0.984601	−	0.174818i	$-0.944066\pi$
$577$	−1.28512e11	−	1.28512e11i	−1.15942	−	1.15942i	−0.174818	−	0.984601i	$-0.555934\pi$
$578$	−3.32128e10	−	3.32128e10i	−0.297574	−	0.297574i
$579$	−3.73945e10	+	3.73945e10i	−0.332731	+	0.332731i
$580$		−	1.68440e11i		−	1.48844i
$581$	−7.44537e10			−0.653404
$582$		−	1.26396e11i		−	1.10164i
$583$		−	3.04576e10i		−	0.263646i
$584$	−1.24099e11	+	1.24099e11i	−1.06688	+	1.06688i
$585$			4.03941e10i			0.344901i
$586$	1.06903e10	−	1.06903e10i	0.0906565	−	0.0906565i
$587$	5.85610e10	−	5.85610e10i	0.493238	−	0.493238i	−0.416087	−	0.909325i	$-0.636599\pi$
$587$	5.85610e10	−	5.85610e10i	0.493238	−	0.493238i	0.909325	+	0.416087i	$0.136599\pi$
$588$	−1.07443e11			−0.898811
$589$	1.21069e11			1.00594
$590$	7.34153e10	+	7.34153e10i	0.605868	+	0.605868i
$591$			1.90490e11i			1.56143i
$592$	3.67161e9	+	1.73541e10i	0.0298930	+	0.141292i
$593$	2.89501e10			0.234116			0.117058	−	0.993125i	$-0.462654\pi$
$593$	2.89501e10			0.234116			0.117058	+	0.993125i	$0.462654\pi$
$594$	2.83629e10	−	2.83629e10i	0.227827	−	0.227827i
$595$			1.25526e11i			1.00153i
$596$		−	8.52103e10i		−	0.675316i
$597$	7.90211e10	+	7.90211e10i	0.622079	+	0.622079i
$598$	−7.23333e10	−	7.23333e10i	−0.565631	−	0.565631i
$599$	2.21598e11			1.72131			0.860654	−	0.509190i	$-0.170055\pi$
$599$	2.21598e11			1.72131			0.860654	+	0.509190i	$0.170055\pi$
$600$	−8.17661e10	−	8.17661e10i	−0.630911	−	0.630911i
$601$	1.90986e11			1.46387			0.731935	−	0.681374i	$-0.238617\pi$
$601$	1.90986e11			1.46387			0.731935	+	0.681374i	$0.238617\pi$
$602$	9.54016e10			0.726390
$603$			1.49817e10i			0.113316i
$604$	−1.23426e11			−0.927380
$605$	6.22715e10	+	6.22715e10i	0.464802	+	0.464802i
$606$	−8.34713e10	+	8.34713e10i	−0.618937	+	0.618937i
$607$	−9.78265e10	+	9.78265e10i	−0.720613	+	0.720613i	−0.968730	−	0.248117i	$-0.920188\pi$
$607$	−9.78265e10	+	9.78265e10i	−0.720613	+	0.720613i	0.248117	+	0.968730i	$0.420188\pi$
$608$	−1.00892e11			−0.738313
$609$	2.63918e11	+	2.63918e11i	1.91866	+	1.91866i
$610$	−3.41412e10	+	3.41412e10i	−0.246581	+	0.246581i
$611$	−4.17253e10	−	4.17253e10i	−0.299388	−	0.299388i
$612$	−1.03146e10	+	1.03146e10i	−0.0735267	+	0.0735267i
$613$		−	6.59871e10i		−	0.467323i	−0.972318	−	0.233661i	$-0.924929\pi$
$613$		−	6.59871e10i		−	0.467323i	0.972318	−	0.233661i	$-0.0750707\pi$
$614$	−2.93258e10	−	2.93258e10i	−0.206337	−	0.206337i
$615$	−2.18039e11	−	2.18039e11i	−1.52417	−	1.52417i
$616$	−1.01713e11	+	1.01713e11i	−0.706407	+	0.706407i
$617$			1.18052e10i			0.0814580i	0.999170	+	0.0407290i	$0.0129680\pi$
$617$			1.18052e10i			0.0814580i	−0.999170	+	0.0407290i	$0.987032\pi$
$618$	1.09656e11			0.751759
$619$			2.00636e11i			1.36662i	0.730130	+	0.683308i	$0.239460\pi$
$619$			2.00636e11i			1.36662i	−0.730130	+	0.683308i	$0.760540\pi$
$620$			1.90858e11i			1.29164i
$621$	−1.40347e11	+	1.40347e11i	−0.943708	+	0.943708i
$622$			1.54749e11i			1.03387i
$623$	−7.99300e10	+	7.99300e10i	−0.530589	+	0.530589i
$624$	−1.49246e10	+	1.49246e10i	−0.0984383	+	0.0984383i
$625$	1.74780e11			1.14544
$626$	−8.96046e10			−0.583490
$627$	6.39720e10	+	6.39720e10i	0.413923	+	0.413923i
$628$		−	4.14391e10i		−	0.266423i
$629$	−4.31193e10	+	6.62608e10i	−0.275467	+	0.423306i
$630$	5.33664e10			0.338771
$631$	1.13020e11	−	1.13020e11i	0.712912	−	0.712912i	−0.254231	−	0.967144i	$-0.581822\pi$
$631$	1.13020e11	−	1.13020e11i	0.712912	−	0.712912i	0.967144	+	0.254231i	$0.0818224\pi$
$632$			2.14844e11i			1.34665i
$633$		−	2.89477e11i		−	1.80301i
$634$	−9.75819e8	−	9.75819e8i	−0.00603966	−	0.00603966i
$635$	−7.91324e10	−	7.91324e10i	−0.486698	−	0.486698i
$636$	−4.67877e10			−0.285959
$637$	−1.13754e11	−	1.13754e11i	−0.690891	−	0.690891i
$638$	1.08558e11			0.655210
$639$	−1.54079e10			−0.0924146
$640$		−	1.77533e11i		−	1.05818i
$641$	−6.32865e10			−0.374868			−0.187434	−	0.982277i	$-0.560017\pi$
$641$	−6.32865e10			−0.374868			−0.187434	+	0.982277i	$0.560017\pi$
$642$	4.65329e10	+	4.65329e10i	0.273918	+	0.273918i
$643$	5.95966e10	−	5.95966e10i	0.348640	−	0.348640i	−0.510963	−	0.859603i	$-0.670711\pi$
$643$	5.95966e10	−	5.95966e10i	0.348640	−	0.348640i	0.859603	+	0.510963i	$0.170711\pi$
$644$	2.03871e11	−	2.03871e11i	1.18526	−	1.18526i
$645$	2.33519e11			1.34922
$646$	−2.51569e10	−	2.51569e10i	−0.144453	−	0.144453i
$647$	4.07840e10	−	4.07840e10i	0.232741	−	0.232741i	−0.581095	−	0.813836i	$-0.697376\pi$
$647$	4.07840e10	−	4.07840e10i	0.232741	−	0.232741i	0.813836	+	0.581095i	$0.197376\pi$
$648$	−1.43363e11	−	1.43363e11i	−0.813086	−	0.813086i
$649$	1.00942e11	−	1.00942e11i	0.568976	−	0.568976i
$650$		−	7.01322e10i		−	0.392884i
$651$	−2.99043e11	−	2.99043e11i	−1.66498	−	1.66498i
$652$	5.77117e10	+	5.77117e10i	0.319355	+	0.319355i
$653$	7.61985e10	−	7.61985e10i	0.419077	−	0.419077i	−0.465808	−	0.884886i	$-0.654236\pi$
$653$	7.61985e10	−	7.61985e10i	0.419077	−	0.419077i	0.884886	+	0.465808i	$0.154236\pi$
$654$			2.39980e10i			0.131179i
$655$	2.27225e11			1.23450
$656$		−	3.74095e10i		−	0.202007i
$657$		−	8.95252e10i		−	0.480489i
$658$	−5.51252e10	+	5.51252e10i	−0.294067	+	0.294067i
$659$			7.40023e10i			0.392377i	0.980566	+	0.196189i	$0.0628565\pi$
$659$			7.40023e10i			0.392377i	−0.980566	+	0.196189i	$0.937144\pi$
$660$	−1.00848e11	+	1.00848e11i	−0.531486	+	0.531486i
$661$	3.42138e10	−	3.42138e10i	0.179223	−	0.179223i	−0.611794	−	0.791017i	$-0.709552\pi$
$661$	3.42138e10	−	3.42138e10i	0.179223	−	0.179223i	0.791017	+	0.611794i	$0.209552\pi$
$662$	1.25217e11			0.651977
$663$	−9.40671e10			−0.486837
$664$	5.80715e10	+	5.80715e10i	0.298738	+	0.298738i
$665$		−	2.77678e11i		−	1.41989i
$666$	2.81703e10	+	1.83318e10i	0.143184	+	0.0931771i
$667$	−5.37177e11			−2.71403
$668$	−1.36397e10	+	1.36397e10i	−0.0685012	+	0.0685012i
$669$		−	1.57985e11i		−	0.788701i
$670$		−	5.76029e10i		−	0.285855i
$671$	4.69423e10	+	4.69423e10i	0.231566	+	0.231566i
$672$	2.49205e11	+	2.49205e11i	1.22202	+	1.22202i
$673$	−3.38677e11			−1.65092			−0.825459	−	0.564463i	$-0.809083\pi$
$673$	−3.38677e11			−1.65092			−0.825459	+	0.564463i	$0.809083\pi$
$674$	8.47468e10	+	8.47468e10i	0.410661	+	0.410661i
$675$	−1.36077e11			−0.655494
$676$	4.07416e10			0.195097
$677$		−	2.22340e10i		−	0.105843i	−0.998599	−	0.0529216i	$-0.983147\pi$
$677$		−	2.22340e10i		−	0.105843i	0.998599	−	0.0529216i	$-0.0168534\pi$
$678$	3.04757e10			0.144223
$679$	3.77172e11	+	3.77172e11i	1.77444	+	1.77444i
$680$	9.79062e10	−	9.79062e10i	0.457904	−	0.457904i
$681$	−2.09495e11	+	2.09495e11i	−0.974058	+	0.974058i
$682$	−1.23007e11			−0.568579
$683$	2.00552e11	+	2.00552e11i	0.921602	+	0.921602i	0.997143	−	0.0755409i	$-0.0240683\pi$
$683$	2.00552e11	+	2.00552e11i	0.921602	+	0.921602i	−0.0755409	+	0.997143i	$0.524068\pi$
$684$	2.28170e10	−	2.28170e10i	0.104240	−	0.104240i
$685$	8.48458e10	+	8.48458e10i	0.385361	+	0.385361i
$686$	−2.03659e10	+	2.03659e10i	−0.0919615	+	0.0919615i
$687$			1.65104e10i			0.0741192i
$688$	2.00327e10	+	2.00327e10i	0.0894099	+	0.0894099i
$689$	−4.95361e10	−	4.95361e10i	−0.219809	−	0.219809i
$690$	−2.33913e11	+	2.33913e11i	−1.03195	+	1.03195i
$691$			3.39783e11i			1.49035i	0.666867	+	0.745177i	$0.267635\pi$
$691$			3.39783e11i			1.49035i	−0.666867	+	0.745177i	$0.732365\pi$
$692$	2.12783e11			0.927924
$693$		−	7.33760e10i		−	0.318142i
$694$		−	2.25842e11i		−	0.973569i
$695$	2.61398e11	−	2.61398e11i	1.12037	−	1.12037i
$696$		−	4.11694e11i		−	1.75444i
$697$	1.17893e11	−	1.17893e11i	0.499524	−	0.499524i
$698$	4.67978e10	−	4.67978e10i	0.197153	−	0.197153i
$699$	−3.82094e11			−1.60052
$700$	1.97668e11			0.823272
$701$	9.16299e10	+	9.16299e10i	0.379459	+	0.379459i	0.870907	−	0.491448i	$-0.163532\pi$
$701$	9.16299e10	+	9.16299e10i	0.379459	+	0.379459i	−0.491448	+	0.870907i	$0.663532\pi$
$702$		−	9.22583e10i		−	0.379889i
$703$	9.53849e10	−	1.46577e11i	0.390534	−	0.600127i
$704$	7.70932e10			0.313853
$705$	−1.34932e11	+	1.34932e11i	−0.546210	+	0.546210i
$706$			1.53517e11i			0.617926i
$707$		−	4.98167e11i		−	1.99387i
$708$	−1.55063e11	−	1.55063e11i	−0.617128	−	0.617128i
$709$	2.16142e11	+	2.16142e11i	0.855369	+	0.855369i	0.990788	−	0.135419i	$-0.0432381\pi$
$709$	2.16142e11	+	2.16142e11i	0.855369	+	0.855369i	−0.135419	+	0.990788i	$0.543238\pi$
$710$	5.92418e10			0.233128
$711$	−7.74944e10	−	7.74944e10i	−0.303244	−	0.303244i
$712$	1.24686e11			0.485173
$713$	6.08671e11			2.35518
$714$			1.24276e11i			0.478185i
$715$	−2.13544e11			−0.817078
$716$	−2.21047e10	−	2.21047e10i	−0.0841069	−	0.0841069i
$717$	3.42401e11	−	3.42401e11i	1.29556	−	1.29556i
$718$	8.41381e10	−	8.41381e10i	0.316588	−	0.316588i
$719$	−1.83577e11			−0.686914			−0.343457	−	0.939168i	$-0.611598\pi$
$719$	−1.83577e11			−0.686914			−0.343457	+	0.939168i	$0.611598\pi$
$720$	1.12060e10	+	1.12060e10i	0.0416986	+	0.0416986i
$721$	−3.27220e11	+	3.27220e11i	−1.21087	+	1.21087i
$722$	−5.28995e10	−	5.28995e10i	−0.194672	−	0.194672i
$723$	3.21373e11	−	3.21373e11i	1.17613	−	1.17613i
$724$			3.99849e10i			0.145527i
$725$	−2.60416e11	−	2.60416e11i	−0.942573	−	0.942573i
$726$	6.16515e10	+	6.16515e10i	0.221921	+	0.221921i
$727$	3.61429e10	−	3.61429e10i	0.129385	−	0.129385i	−0.639449	−	0.768834i	$-0.720837\pi$
$727$	3.61429e10	−	3.61429e10i	0.129385	−	0.129385i	0.768834	+	0.639449i	$0.220837\pi$
$728$			3.30851e11i			1.17790i
$729$	−1.53181e11			−0.542370
$730$			3.44215e11i			1.21210i
$731$			1.26263e11i			0.442186i
$732$	7.21107e10	−	7.21107e10i	0.251163	−	0.251163i
$733$			1.89898e11i			0.657815i	0.944362	+	0.328908i	$0.106680\pi$
$733$			1.89898e11i			0.657815i	−0.944362	+	0.328908i	$0.893320\pi$
$734$	5.27748e10	−	5.27748e10i	0.181820	−	0.181820i
$735$	−3.67861e11	+	3.67861e11i	−1.26048	+	1.26048i
$736$	−5.07230e11			−1.72860
$737$	−7.92010e10			−0.268448
$738$	−5.01212e10	−	5.01212e10i	−0.168965	−	0.168965i
$739$		−	2.48818e11i		−	0.834266i	−0.908846	−	0.417133i	$-0.863035\pi$
$739$		−	2.48818e11i		−	0.834266i	0.908846	−	0.417133i	$-0.136965\pi$
$740$	2.31069e11	+	1.50369e11i	0.770576	+	0.501453i
$741$	2.08087e11			0.690196
$742$	−6.54443e10	+	6.54443e10i	−0.215902	+	0.215902i
$743$		−	1.15452e11i		−	0.378831i	−0.981897	−	0.189416i	$-0.939341\pi$
$743$		−	1.15452e11i		−	0.378831i	0.981897	−	0.189416i	$-0.0606594\pi$
$744$			4.66487e11i			1.52247i
$745$	−2.91742e11	−	2.91742e11i	−0.947051	−	0.947051i
$746$	−1.11511e11	−	1.11511e11i	−0.360049	−	0.360049i
$747$	−4.18928e10			−0.134542
$748$	−5.45282e10	−	5.45282e10i	−0.174186	−	0.174186i
$749$	−2.77714e11			−0.882410
$750$	4.86569e10			0.153780
$751$			3.52663e11i			1.10866i	0.832296	+	0.554332i	$0.187026\pi$
$751$			3.52663e11i			1.10866i	−0.832296	+	0.554332i	$0.812974\pi$
$752$	−2.31507e10			−0.0723922
$753$	−1.31583e10	−	1.31583e10i	−0.0409278	−	0.0409278i
$754$	1.76559e11	−	1.76559e11i	0.546265	−	0.546265i
$755$	−4.22583e11	+	4.22583e11i	−1.30054	+	1.30054i
$756$	2.60030e11			0.796042
$757$	2.81681e11	+	2.81681e11i	0.857775	+	0.857775i	0.991076	−	0.133301i	$-0.0425576\pi$
$757$	2.81681e11	+	2.81681e11i	0.857775	+	0.857775i	−0.133301	+	0.991076i	$0.542558\pi$
$758$	1.71547e11	−	1.71547e11i	0.519644	−	0.519644i
$759$	3.21618e11	+	3.21618e11i	0.969111	+	0.969111i
$760$	−2.16580e11	+	2.16580e11i	−0.649177	+	0.649177i
$761$		−	3.84115e11i		−	1.14531i	−0.819796	−	0.572655i	$-0.805913\pi$
$761$		−	3.84115e11i		−	1.14531i	0.819796	−	0.572655i	$-0.194087\pi$
$762$	−7.83446e10	−	7.83446e10i	−0.232375	−	0.232375i
$763$	−7.16114e10	−	7.16114e10i	−0.211293	−	0.211293i
$764$	−1.34091e11	+	1.34091e11i	−0.393575	+	0.393575i
$765$			7.06296e10i			0.206225i
$766$	−2.28092e10			−0.0662513
$767$		−	3.28343e11i		−	0.948738i
$768$		−	3.49704e11i		−	1.00521i
$769$	−2.75233e10	+	2.75233e10i	−0.0787038	+	0.0787038i	−0.745363	−	0.666659i	$-0.767724\pi$
$769$	−2.75233e10	+	2.75233e10i	−0.0787038	+	0.0787038i	0.666659	+	0.745363i	$0.267724\pi$
$770$			2.82123e11i			0.802556i
$771$	3.28228e11	−	3.28228e11i	0.928878	−	0.928878i
$772$	−7.05093e10	+	7.05093e10i	−0.198508	+	0.198508i
$773$	−1.28534e11			−0.359999			−0.179999	−	0.983667i	$-0.557610\pi$
$773$	−1.28534e11			−0.359999			−0.179999	+	0.983667i	$0.557610\pi$
$774$	5.36795e10			0.149570
$775$	2.95075e11	+	2.95075e11i	0.817947	+	0.817947i
$776$		−	5.88363e11i		−	1.62255i
$777$	−5.97651e11	+	1.26445e11i	−1.63970	+	0.346910i
$778$	−7.28202e9			−0.0198762
$779$	−2.60792e11	+	2.60792e11i	−0.708182	+	0.708182i
$780$			3.28037e11i			0.886226i
$781$		−	8.14543e10i		−	0.218932i
$782$	−1.26476e11	−	1.26476e11i	−0.338205	−	0.338205i
$783$	−3.42574e11	−	3.42574e11i	−0.911397	−	0.911397i
$784$	−6.31148e10			−0.167058
$785$	−1.41878e11	−	1.41878e11i	−0.373627	−	0.373627i
$786$	2.24962e11			0.589413
$787$	−2.15823e11			−0.562600			−0.281300	−	0.959620i	$-0.590766\pi$
$787$	−2.15823e11			−0.562600			−0.281300	+	0.959620i	$0.590766\pi$
$788$			3.59179e11i			0.931550i
$789$	2.28501e11			0.589631
$790$	2.97958e11	+	2.97958e11i	0.764973	+	0.764973i
$791$	−9.09412e10	+	9.09412e10i	−0.232303	+	0.232303i
$792$	−5.72309e10	+	5.72309e10i	−0.145455	+	0.145455i
$793$	1.52693e11			0.386124
$794$	−5.54721e10	−	5.54721e10i	−0.139570	−	0.139570i
$795$	−1.60191e11	+	1.60191e11i	−0.401023	+	0.401023i
$796$	1.48998e11	+	1.48998e11i	0.371133	+	0.371133i
$797$	−2.86051e11	+	2.86051e11i	−0.708941	+	0.708941i	−0.966312	−	0.257372i	$-0.917143\pi$
$797$	−2.86051e11	+	2.86051e11i	−0.708941	+	0.708941i	0.257372	+	0.966312i	$0.417143\pi$
$798$		−	2.74913e11i		−	0.677929i
$799$	−7.29573e10	−	7.29573e10i	−0.179012	−	0.179012i
$800$	−2.45898e11	−	2.45898e11i	−0.600337	−	0.600337i
$801$	−4.49741e10	+	4.49741e10i	−0.109253	+	0.109253i
$802$		−	3.98636e11i		−	0.963561i
$803$	4.73277e11			1.13829
$804$			1.21665e11i			0.291167i
$805$		−	1.39602e12i		−	3.32436i
$806$	−2.00057e11	+	2.00057e11i	−0.474039	+	0.474039i
$807$			7.42280e11i			1.75014i
$808$	−3.88554e11	+	3.88554e11i	−0.911602	+	0.911602i
$809$	1.64448e10	−	1.64448e10i	0.0383914	−	0.0383914i	−0.687650	−	0.726042i	$-0.741358\pi$
$809$	1.64448e10	−	1.64448e10i	0.0383914	−	0.0383914i	0.726042	+	0.687650i	$0.241358\pi$
$810$	−3.97646e11			−0.923755
$811$	6.00941e11			1.38915			0.694574	−	0.719422i	$-0.255593\pi$
$811$	6.00941e11			1.38915			0.694574	+	0.719422i	$0.255593\pi$
$812$	4.97630e11	+	4.97630e11i	1.14468	+	1.14468i
$813$			1.88174e11i			0.430723i
$814$	−9.69117e10	+	1.48923e11i	−0.220739	+	0.339206i
$815$	3.95184e11			0.895714
$816$	−2.60959e10	+	2.60959e10i	−0.0588588	+	0.0588588i
$817$		−	2.79307e11i		−	0.626894i
$818$			3.14068e11i			0.701472i
$819$	−1.19338e11	−	1.19338e11i	−0.265243	−	0.265243i
$820$	−4.11124e11	−	4.11124e11i	−0.909320	−	0.909320i
$821$	−1.60550e11			−0.353376			−0.176688	−	0.984267i	$-0.556538\pi$
$821$	−1.60550e11			−0.353376			−0.176688	+	0.984267i	$0.556538\pi$
$822$	8.40011e10	+	8.40011e10i	0.183991	+	0.183991i
$823$	4.77248e11			1.04027			0.520134	−	0.854085i	$-0.325882\pi$
$823$	4.77248e11			1.04027			0.520134	+	0.854085i	$0.325882\pi$
$824$	5.10442e11			1.10723
$825$			3.11832e11i			0.673138i
$826$	−4.33789e11			−0.931876
$827$	−2.51612e11	−	2.51612e11i	−0.537911	−	0.537911i	0.385004	−	0.922915i	$-0.374200\pi$
$827$	−2.51612e11	−	2.51612e11i	−0.537911	−	0.537911i	−0.922915	+	0.385004i	$0.874200\pi$
$828$	1.14712e11	−	1.14712e11i	0.244055	−	0.244055i
$829$	1.00988e11	−	1.00988e11i	0.213822	−	0.213822i	−0.592067	−	0.805889i	$-0.701688\pi$
$829$	1.00988e11	−	1.00988e11i	0.213822	−	0.213822i	0.805889	+	0.592067i	$0.201688\pi$
$830$	1.61073e11			0.339399
$831$	−2.03670e11	−	2.03670e11i	−0.427094	−	0.427094i
$832$	1.25384e11	−	1.25384e11i	0.261667	−	0.261667i
$833$	−1.98901e11	−	1.98901e11i	−0.413102	−	0.413102i
$834$	2.58796e11	−	2.58796e11i	0.534925	−	0.534925i
$835$			9.33985e10i			0.192130i
$836$	1.20623e11	+	1.20623e11i	0.246947	+	0.246947i
$837$	3.88168e11	+	3.88168e11i	0.790893	+	0.790893i
$838$	−2.61239e11	+	2.61239e11i	−0.529739	+	0.529739i
$839$			5.37523e11i			1.08480i	0.840121	+	0.542399i	$0.182484\pi$
$839$			5.37523e11i			1.08480i	−0.840121	+	0.542399i	$0.817516\pi$
$840$	1.06991e12			2.14898
$841$		−	8.10951e11i		−	1.62110i
$842$		−	4.80605e11i		−	0.956180i
$843$	−4.52193e11	+	4.52193e11i	−0.895393	+	0.895393i
$844$		−	5.45823e11i		−	1.07568i
$845$	1.39490e11	−	1.39490e11i	0.273601	−	0.273601i
$846$	−3.10172e10	+	3.10172e10i	−0.0605510	+	0.0605510i
$847$	−3.67944e11			−0.714904
$848$	−2.74843e10			−0.0531498
$849$	6.96880e11	+	6.96880e11i	1.34130	+	1.34130i
$850$		−	1.22627e11i		−	0.234915i
$851$	4.79546e11	−	7.36911e11i	0.914349	−	1.40507i
$852$	−1.25127e11			−0.237461
$853$	−5.26088e11	+	5.26088e11i	−0.993716	+	0.993716i	−0.999980	−	0.00626450i	$-0.998006\pi$
$853$	−5.26088e11	+	5.26088e11i	−0.993716	+	0.993716i	0.00626450	+	0.999980i	$0.498006\pi$
$854$		−	2.01730e11i		−	0.379261i
$855$		−	1.56241e11i		−	0.292368i
$856$	2.16608e11	+	2.16608e11i	0.403440	+	0.403440i
$857$	2.00906e11	+	2.00906e11i	0.372452	+	0.372452i	0.868369	−	0.495918i	$-0.165168\pi$
$857$	2.00906e11	+	2.00906e11i	0.372452	+	0.372452i	−0.495918	+	0.868369i	$0.665168\pi$
$858$	−2.11418e11			−0.390115
$859$	−3.14438e11	−	3.14438e11i	−0.577514	−	0.577514i	0.356704	−	0.934218i	$-0.383901\pi$
$859$	−3.14438e11	−	3.14438e11i	−0.577514	−	0.577514i	−0.934218	+	0.356704i	$0.883901\pi$
$860$	4.40311e11			0.804945
$861$	1.28833e12			2.34430
$862$			5.16938e10i			0.0936288i
$863$	−2.90734e11			−0.524146			−0.262073	−	0.965048i	$-0.584406\pi$
$863$	−2.90734e11			−0.524146			−0.262073	+	0.965048i	$0.584406\pi$
$864$	−3.23476e11	−	3.23476e11i	−0.580481	−	0.580481i
$865$	7.28522e11	−	7.28522e11i	1.30130	−	1.30130i
$866$	−3.18322e11	+	3.18322e11i	−0.565972	+	0.565972i
$867$	4.80356e11			0.850133
$868$	−5.63860e11	−	5.63860e11i	−0.993328	−	0.993328i
$869$	4.09676e11	−	4.09676e11i	0.718392	−	0.718392i
$870$	−5.70959e11	−	5.70959e11i	−0.996617	−	0.996617i
$871$	−1.28812e11	+	1.28812e11i	−0.223812	+	0.223812i
$872$			1.11709e11i			0.193207i
$873$	2.12223e11	+	2.12223e11i	0.365372	+	0.365372i
$874$	2.79779e11	+	2.79779e11i	0.479479	+	0.479479i
$875$	−1.45195e11	+	1.45195e11i	−0.247696	+	0.247696i
$876$		−	7.27028e11i		−	1.23462i
$877$	−9.12199e11			−1.54202			−0.771012	−	0.636821i	$-0.780249\pi$
$877$	−9.12199e11			−1.54202			−0.771012	+	0.636821i	$0.780249\pi$
$878$		−	3.94494e11i		−	0.663838i
$879$			1.54613e11i			0.258995i
$880$	−5.92409e10	+	5.92409e10i	−0.0987849	+	0.0987849i
$881$		−	3.58492e11i		−	0.595081i	−0.954709	−	0.297541i	$-0.903834\pi$
$881$		−	3.58492e11i		−	0.595081i	0.954709	−	0.297541i	$-0.0961664\pi$
$882$	−8.45611e10	+	8.45611e10i	−0.139732	+	0.139732i
$883$	−8.07021e10	+	8.07021e10i	−0.132752	+	0.132752i	−0.770361	−	0.637608i	$-0.779924\pi$
$883$	−8.07021e10	+	8.07021e10i	−0.132752	+	0.132752i	0.637608	+	0.770361i	$0.279924\pi$
$884$	−1.77368e11			−0.290447
$885$	−1.06180e12			−1.73090
$886$	3.32720e11	+	3.32720e11i	0.539938	+	0.539938i
$887$		−	8.69001e11i		−	1.40387i	−0.712243	−	0.701933i	$-0.752321\pi$
$887$		−	8.69001e11i		−	1.40387i	0.712243	−	0.701933i	$-0.247679\pi$
$888$	5.64771e11	+	3.67525e11i	0.908281	+	0.591065i
$889$	4.67570e11			0.748582
$890$	1.72921e11	−	1.72921e11i	0.275605	−	0.275605i
$891$			5.46743e11i			0.867505i
$892$		−	2.97889e11i		−	0.470539i
$893$	1.61390e11	+	1.61390e11i	0.253788	+	0.253788i
$894$	−2.88837e11	−	2.88837e11i	−0.452171	−	0.452171i
$895$	−1.51363e11			−0.235900
$896$	5.24494e11	+	5.24494e11i	0.813782	+	0.813782i
$897$	1.04615e12			1.61594
$898$	8.45610e10			0.130036
$899$			1.48571e12i			2.27454i
$900$	1.11221e11			0.169519
$901$	−8.66145e10	−	8.66145e10i	−0.131429	−	0.131429i
$902$	2.64967e11	−	2.64967e11i	0.400281	−	0.400281i
$903$	−6.89896e11	+	6.89896e11i	−1.03761	+	1.03761i
$904$	1.41862e11			0.212419
$905$	1.36900e11	+	1.36900e11i	0.204084	+	0.204084i
$906$	−4.18375e11	+	4.18375e11i	−0.620945	+	0.620945i
$907$	2.90253e11	+	2.90253e11i	0.428891	+	0.428891i	0.888251	−	0.459359i	$-0.151921\pi$
$907$	2.90253e11	+	2.90253e11i	0.428891	+	0.428891i	−0.459359	+	0.888251i	$0.651921\pi$
$908$	−3.95013e11	+	3.95013e11i	−0.581123	+	0.581123i
$909$		−	2.80303e11i		−	0.410555i
$910$	4.58842e11	+	4.58842e11i	0.669110	+	0.669110i
$911$	−1.48209e11	−	1.48209e11i	−0.215180	−	0.215180i	0.591284	−	0.806464i	$-0.298621\pi$
$911$	−1.48209e11	−	1.48209e11i	−0.215180	−	0.215180i	−0.806464	+	0.591284i	$0.798621\pi$
$912$	5.77271e10	−	5.77271e10i	0.0834449	−	0.0834449i
$913$		−	2.21467e11i		−	0.318732i
$914$	−3.28194e11			−0.470268
$915$		−	4.93783e11i		−	0.704452i
$916$			3.11312e10i			0.0442195i
$917$	−6.71301e11	+	6.71301e11i	−0.949380	+	0.949380i
$918$		−	1.61315e11i		−	0.227145i
$919$	−8.52655e11	+	8.52655e11i	−1.19539	+	1.19539i	−0.219864	+	0.975531i	$0.570561\pi$
$919$	−8.52655e11	+	8.52655e11i	−1.19539	+	1.19539i	−0.975531	+	0.219864i	$0.929439\pi$
$920$	−1.08885e12	+	1.08885e12i	−1.51991	+	1.51991i
$921$	4.24138e11			0.589480
$922$	−2.64407e11			−0.365888
$923$	−1.32477e11	−	1.32477e11i	−0.182529	−	0.182529i
$924$		−	5.95881e11i		−	0.817470i
$925$	5.89720e11	−	1.24767e11i	0.805525	−	0.170425i
$926$	5.22224e11			0.710253
$927$	−1.84117e11	+	1.84117e11i	−0.249330	+	0.249330i
$928$		−	1.23810e12i		−	1.66941i
$929$			2.63990e11i			0.354425i	0.984173	+	0.177212i	$0.0567079\pi$
$929$			2.63990e11i			0.354425i	−0.984173	+	0.177212i	$0.943292\pi$
$930$	6.46949e11	+	6.46949e11i	0.864845	+	0.864845i
$931$	4.39992e11	+	4.39992e11i	0.585660	+	0.585660i
$932$	−7.20458e11			−0.954872
$933$	−1.11907e12	−	1.11907e12i	−1.47683	−	1.47683i
$934$	−7.74657e11			−1.01794
$935$	−3.73385e11			−0.488552
$936$			1.86160e11i			0.242539i
$937$	8.76784e11			1.13746			0.568728	−	0.822526i	$-0.307436\pi$
$937$	8.76784e11			1.13746			0.568728	+	0.822526i	$0.307436\pi$
$938$	1.70179e11	+	1.70179e11i	0.219834	+	0.219834i
$939$	6.47975e11	−	6.47975e11i	0.833481	−	0.833481i
$940$	−2.54422e11	+	2.54422e11i	−0.325869	+	0.325869i
$941$	−8.24980e11			−1.05217			−0.526084	−	0.850433i	$-0.676340\pi$
$941$	−8.24980e11			−1.05217			−0.526084	+	0.850433i	$0.676340\pi$
$942$	−1.40466e11	−	1.40466e11i	−0.178389	−	0.178389i
$943$	−1.31113e12	+	1.31113e12i	−1.65805	+	1.65805i
$944$	−9.10881e10	−	9.10881e10i	−0.114703	−	0.114703i
$945$	8.90285e11	−	8.90285e11i	1.11635	−	1.11635i
$946$			2.83778e11i			0.354335i
$947$	−5.38834e11	−	5.38834e11i	−0.669970	−	0.669970i	0.287739	−	0.957709i	$-0.407096\pi$
$947$	−5.38834e11	−	5.38834e11i	−0.669970	−	0.669970i	−0.957709	+	0.287739i	$0.907096\pi$
$948$	−6.29327e11	−	6.29327e11i	−0.779189	−	0.779189i
$949$	7.69734e11	−	7.69734e11i	0.949021	−	0.949021i
$950$			2.71266e11i			0.333043i
$951$	1.41133e10			0.0172546
$952$			5.78498e11i			0.704295i
$953$			2.49080e11i			0.301972i	0.988536	+	0.150986i	$0.0482448\pi$
$953$			2.49080e11i			0.301972i	−0.988536	+	0.150986i	$0.951755\pi$
$954$	−3.68235e10	+	3.68235e10i	−0.0444561	+	0.0444561i
$955$			9.18199e11i			1.10388i
$956$	6.45614e11	−	6.45614e11i	0.772932	−	0.772932i
$957$	−7.85039e11	+	7.85039e11i	−0.935930	+	0.935930i
$958$	2.74647e11			0.326071
$959$	−5.01329e11			−0.592718
$960$	−4.05469e11	−	4.05469e11i	−0.477390	−	0.477390i
$961$		−	8.30551e11i		−	0.973807i
$962$	8.45904e10	+	3.99823e11i	0.0987690	+	0.466840i
$963$	−1.56261e11			−0.181696
$964$	6.05966e11	−	6.05966e11i	0.701682	−	0.701682i
$965$			4.82817e11i			0.556767i
$966$		−	1.38212e12i		−	1.58722i
$967$	1.90992e10	+	1.90992e10i	0.0218428	+	0.0218428i	0.717944	−	0.696101i	$-0.245083\pi$
$967$	1.90992e10	+	1.90992e10i	0.0218428	+	0.0218428i	−0.696101	+	0.717944i	$0.745083\pi$
$968$	2.86984e11	+	2.86984e11i	0.326856	+	0.326856i
$969$	3.63844e11			0.412686
$970$	−8.15973e11	−	8.15973e11i	−0.921699	−	0.921699i
$971$	−1.14400e11			−0.128691			−0.0643456	−	0.997928i	$-0.520496\pi$
$971$	−1.14400e11			−0.128691			−0.0643456	+	0.997928i	$0.520496\pi$
$972$	3.56044e11			0.398876
$973$			1.54452e12i			1.72323i
$974$	−6.58190e11			−0.731333
$975$	5.07160e11	+	5.07160e11i	0.561212	+	0.561212i
$976$	4.23598e10	−	4.23598e10i	0.0466825	−	0.0466825i
$977$	−6.99163e11	+	6.99163e11i	−0.767362	+	0.767362i	−0.977641	−	0.210280i	$-0.932563\pi$
$977$	−6.99163e11	+	6.99163e11i	−0.767362	+	0.767362i	0.210280	+	0.977641i	$0.432563\pi$
$978$	3.91250e11			0.427660
$979$	−2.37757e11	−	2.37757e11i	−0.258823	−	0.258823i
$980$	−6.93621e11	+	6.93621e11i	−0.752000	+	0.752000i
$981$	−4.02935e10	−	4.02935e10i	−0.0435070	−	0.0435070i
$982$	4.45649e10	−	4.45649e10i	0.0479233	−	0.0479233i
$983$		−	1.14820e12i		−	1.22971i	−0.788640	−	0.614855i	$-0.789215\pi$
$983$		−	1.14820e12i		−	1.22971i	0.788640	−	0.614855i	$-0.210785\pi$
$984$	−1.00485e12	−	1.00485e12i	−1.07182	−	1.07182i
$985$	1.22975e12	+	1.22975e12i	1.30639	+	1.30639i
$986$	3.08715e11	−	3.08715e11i	0.326626	−	0.326626i
$987$		−	7.97274e11i		−	0.840116i
$988$	3.92359e11			0.411771
$989$		−	1.40421e12i		−	1.46773i
$990$			1.58742e11i			0.165253i
$991$	1.71417e11	−	1.71417e11i	0.177730	−	0.177730i	−0.612636	−	0.790365i	$-0.709891\pi$
$991$	1.71417e11	−	1.71417e11i	0.177730	−	0.177730i	0.790365	+	0.612636i	$0.209891\pi$
$992$			1.40288e12i			1.44869i
$993$	−9.05507e11	+	9.05507e11i	−0.931312	+	0.931312i
$994$	−1.75021e11	+	1.75021e11i	−0.179285	+	0.179285i
$995$	1.02028e12			1.04094
$996$	−3.40208e11			−0.345706
$997$	1.20645e12	+	1.20645e12i	1.22103	+	1.22103i	0.967265	+	0.253768i	$0.0816699\pi$
$997$	1.20645e12	+	1.20645e12i	1.22103	+	1.22103i	0.253768	+	0.967265i	$0.418330\pi$
$998$			5.33543e11i			0.537833i
$999$	7.75772e11	−	1.64130e11i	0.778883	−	0.164788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.9.d.a.6.16	✓	50
37.31	odd	4	inner	37.9.d.a.31.16	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.9.d.a.6.16	✓	50	1.1	even	1	trivial
37.9.d.a.31.16	yes	50	37.31	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	37.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(6.39144 - 6.39144i) q^{2} +92.4393i q^{3} +174.299i q^{4} +(596.761 + 596.761i) q^{5} +(590.820 + 590.820i) q^{6} -3526.08 q^{7} +(2750.23 + 2750.23i) q^{8} -1984.02 q^{9} +O(q^{10})\)	\(q+(6.39144 - 6.39144i) q^{2} +92.4393i q^{3} +174.299i q^{4} +(596.761 + 596.761i) q^{5} +(590.820 + 590.820i) q^{6} -3526.08 q^{7} +(2750.23 + 2750.23i) q^{8} -1984.02 q^{9} +7628.33 q^{10} -10488.6i q^{11} -16112.1 q^{12} +(-17058.5 - 17058.5i) q^{13} +(-22536.8 + 22536.8i) q^{14} +(-55164.2 + 55164.2i) q^{15} -9464.66 q^{16} +(-29827.1 - 29827.1i) q^{17} +(-12680.7 + 12680.7i) q^{18} +(65980.9 + 65980.9i) q^{19} +(-104015. + 104015. i) q^{20} -325949. i q^{21} +(-67037.0 - 67037.0i) q^{22} +(331717. + 331717. i) q^{23} +(-254229. + 254229. i) q^{24} +321624. i q^{25} -218057. q^{26} +423093. i q^{27} -614593. i q^{28} +(-809690. + 809690. i) q^{29} +705157. i q^{30} +(917454. - 917454. i) q^{31} +(-764552. + 764552. i) q^{32} +969554. q^{33} -381276. q^{34} +(-2.10423e6 - 2.10423e6i) q^{35} -345812. i q^{36} +(-387928. - 1.83357e6i) q^{37} +843425. q^{38} +(1.57688e6 - 1.57688e6i) q^{39} +3.28246e6i q^{40} +3.95254e6i q^{41} +(-2.08328e6 - 2.08328e6i) q^{42} +(-2.11658e6 - 2.11658e6i) q^{43} +1.82814e6 q^{44} +(-1.18399e6 - 1.18399e6i) q^{45} +4.24031e6 q^{46} +2.44601e6 q^{47} -874906. i q^{48} +6.66847e6 q^{49} +(2.05564e6 + 2.05564e6i) q^{50} +(2.75719e6 - 2.75719e6i) q^{51} +(2.97328e6 - 2.97328e6i) q^{52} +2.90389e6 q^{53} +(2.70417e6 + 2.70417e6i) q^{54} +(6.25917e6 - 6.25917e6i) q^{55} +(-9.69755e6 - 9.69755e6i) q^{56} +(-6.09922e6 + 6.09922e6i) q^{57} +1.03502e7i q^{58} +(9.62403e6 + 9.62403e6i) q^{59} +(-9.61506e6 - 9.61506e6i) q^{60} +(-4.47557e6 + 4.47557e6i) q^{61} -1.17277e7i q^{62} +6.99582e6 q^{63} +7.35022e6i q^{64} -2.03597e7i q^{65} +(6.19685e6 - 6.19685e6i) q^{66} -7.55118e6i q^{67} +(5.19882e6 - 5.19882e6i) q^{68} +(-3.06637e7 + 3.06637e7i) q^{69} -2.68981e7 q^{70} +7.76602e6 q^{71} +(-5.45651e6 - 5.45651e6i) q^{72} +4.51232e7i q^{73} +(-1.41986e7 - 9.23976e6i) q^{74} -2.97306e7 q^{75} +(-1.15004e7 + 1.15004e7i) q^{76} +3.69835e7i q^{77} -2.01570e7i q^{78} +(3.90593e7 + 3.90593e7i) q^{79} +(-5.64814e6 - 5.64814e6i) q^{80} -5.21275e7 q^{81} +(2.52625e7 + 2.52625e7i) q^{82} +2.11151e7 q^{83} +5.68125e7 q^{84} -3.55993e7i q^{85} -2.70560e7 q^{86} +(-7.48472e7 - 7.48472e7i) q^{87} +(2.88459e7 - 2.88459e7i) q^{88} +(2.26682e7 - 2.26682e7i) q^{89} -1.51347e7 q^{90} +(6.01497e7 + 6.01497e7i) q^{91} +(-5.78180e7 + 5.78180e7i) q^{92} +(8.48087e7 + 8.48087e7i) q^{93} +(1.56335e7 - 1.56335e7i) q^{94} +7.87497e7i q^{95} +(-7.06746e7 - 7.06746e7i) q^{96} +(-1.06966e8 - 1.06966e8i) q^{97} +(4.26212e7 - 4.26212e7i) q^{98} +2.08095e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 4 q^{2} + 124 q^{5} + 510 q^{6} - 4 q^{7} - 5256 q^{8} - 93534 q^{9}+O(q^{10}) \) 50 * q + 4 * q^2 + 124 * q^5 + 510 * q^6 - 4 * q^7 - 5256 * q^8 - 93534 * q^9	\( 50 q + 4 q^{2} + 124 q^{5} + 510 q^{6} - 4 q^{7} - 5256 q^{8} - 93534 q^{9} - 10756 q^{10} - 45440 q^{12} + 63592 q^{13} - 80206 q^{14} - 124346 q^{15} - 639128 q^{16} - 178796 q^{17} - 45882 q^{18} + 264774 q^{19} + 469204 q^{20} + 714574 q^{22} - 654272 q^{23} - 1573644 q^{24} + 1841660 q^{26} - 1683686 q^{29} + 1766336 q^{31} - 4332632 q^{32} - 1438888 q^{33} - 5838452 q^{34} - 650482 q^{35} - 2870078 q^{37} - 2281528 q^{38} + 11036546 q^{39} - 7453902 q^{42} + 5097830 q^{43} - 14992464 q^{44} - 15078446 q^{45} + 28776464 q^{46} + 13992320 q^{47} + 4370314 q^{49} + 7603288 q^{50} + 19417938 q^{51} + 54318452 q^{52} + 28075952 q^{53} - 19197122 q^{54} - 6104306 q^{55} + 47803128 q^{56} + 17462426 q^{57} - 677072 q^{59} + 24953316 q^{60} + 4206386 q^{61} - 18098032 q^{63} - 56061730 q^{66} - 52579760 q^{68} + 88118984 q^{69} - 295493636 q^{70} - 37172476 q^{71} - 74582504 q^{72} - 224754524 q^{74} - 144364996 q^{75} + 189294548 q^{76} + 271163438 q^{79} - 312998084 q^{80} + 41535626 q^{81} - 177494710 q^{82} - 74250268 q^{83} - 82088924 q^{84} + 112964036 q^{86} - 142771908 q^{87} + 224951860 q^{88} + 84928780 q^{89} + 716592116 q^{90} - 40969098 q^{91} - 701292428 q^{92} - 83761576 q^{93} + 553881406 q^{94} - 7259376 q^{96} + 467792674 q^{97} + 538649310 q^{98}+O(q^{100}) \) 50 * q + 4 * q^2 + 124 * q^5 + 510 * q^6 - 4 * q^7 - 5256 * q^8 - 93534 * q^9 - 10756 * q^10 - 45440 * q^12 + 63592 * q^13 - 80206 * q^14 - 124346 * q^15 - 639128 * q^16 - 178796 * q^17 - 45882 * q^18 + 264774 * q^19 + 469204 * q^20 + 714574 * q^22 - 654272 * q^23 - 1573644 * q^24 + 1841660 * q^26 - 1683686 * q^29 + 1766336 * q^31 - 4332632 * q^32 - 1438888 * q^33 - 5838452 * q^34 - 650482 * q^35 - 2870078 * q^37 - 2281528 * q^38 + 11036546 * q^39 - 7453902 * q^42 + 5097830 * q^43 - 14992464 * q^44 - 15078446 * q^45 + 28776464 * q^46 + 13992320 * q^47 + 4370314 * q^49 + 7603288 * q^50 + 19417938 * q^51 + 54318452 * q^52 + 28075952 * q^53 - 19197122 * q^54 - 6104306 * q^55 + 47803128 * q^56 + 17462426 * q^57 - 677072 * q^59 + 24953316 * q^60 + 4206386 * q^61 - 18098032 * q^63 - 56061730 * q^66 - 52579760 * q^68 + 88118984 * q^69 - 295493636 * q^70 - 37172476 * q^71 - 74582504 * q^72 - 224754524 * q^74 - 144364996 * q^75 + 189294548 * q^76 + 271163438 * q^79 - 312998084 * q^80 + 41535626 * q^81 - 177494710 * q^82 - 74250268 * q^83 - 82088924 * q^84 + 112964036 * q^86 - 142771908 * q^87 + 224951860 * q^88 + 84928780 * q^89 + 716592116 * q^90 - 40969098 * q^91 - 701292428 * q^92 - 83761576 * q^93 + 553881406 * q^94 - 7259376 * q^96 + 467792674 * q^97 + 538649310 * q^98

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